We (Queensland, Australia) had new e-scooter laws brought in late last year, none of which is signposted anywhere, just written into legislation
Basically, you can ride at a maximum 25kph, on the road, if the road has a speed limit of 50kph or lower.
If the road limit is above 50, then e-scooters must only be ridden on the footpath at a max 12kph.
Not the faintest idea how we’d map any of that in OSM! 
Not the faintest idea how we’d map any of that in OSM!
as you wrote: „ none of which is signposted anywhere, just written into legislation“ one possibility is not to map it at all, because it’s a default and not reflected on the ground
I’ve got an example where a bike lane takes the sidewalk to pass under a highway underpass. The end of the lane uses pictograms with arrows to direct bikes onto the sidewalk:
https://www.mapillary.com/app/?pKey=521614586719872
At the end of the designated shared sidewalk, the green bike sign is used with an ENDS plate.
https://www.mapillary.com/app/?pKey=645032137380083
Unfortunately most installations aren’t even this clear. It’s common for a bike lane to end at a large intersection or a roundabout with a dedicated ramp onto the sidewalk but no signage or markings whatsoever.
If a max 50 sign indicates (under this legislation) that e-scooters may ride there, you can tag that, I think. I wouldn’t rely on country-specific defaults, or as little as possible.
Signage is always a combination of country specific signs and legislation. If you can translate the effects of this contry specific combination to OSM-wide access tags, all data users can use this without having to know the country-specific signs and regulations.
Additionally, cycling is allowed on the sidewalk if the speed limit on the adjacent carriageway exceeds 50 km/h, and the width of the sidewalk is at least 2 m. Should these also be tagged as foot=designated + bicycle=yes?
How can the cyclist know this? Is there always a speed limit sign, or is it the absence of a speed limit sign?
Inside built-up area you’d need a sign raising the speed limit above the default of 50 km/h.
Outside built-up area the default limit is 90 km/h, so the absence of a speed limit sign is enough.
I think that is enough ground truth to warrant bicycle=yes on a separate sidewalk way.
If the way is highway=footway or highway=pedestrian, foot=designated is implied so you there is no point in tagging that explicitly.
If one were to do that (which seems to be depending on point of view of specific mapper), I’d definitely highly recommend also adding bicycle:signed=no in such cases - to differentiate such “implied by (current) law” cases from those which are explicitly signed (i.e. with bicycle:signed=yes, as would be tagged by that StreetComplete answer “Footway, but a sign allows cycling” for example)
There’s no such concept in Finland; if something’s signed as a footway, bikes are not allowed; it would need to be changed to designated shared use path.
Maybe I’ll show my tagging noobness, but I’ve been wondering for a while whether “designated” is merely a synonym for “signed”, or if it refers to additional that don’t imply a sign (I’m counting as a sign any kind of visual indication of the access level, be it a vertical sign, a painted symbol in the ground, etc.)
I sometimes get the impression that “designated” is used to refer to the legal status of a way, but people in this thread have already suggested that legal determinations should not be mapped if they are not visible on the ground for surveyors.
If, otherwise, we can consider “designated” as a synonym for “signed”, then using bicycle:signed might introduce further confusion by using a different term and therefore suggesting that “designated” means something more (or other) than “signed”.
Something can be designated for a certain mode of transport without being signed. Best example are sidewalks, which are designated for pedestrians.
Germany (specifically?) has this concept of non-compulsory bike paths. They are clearly recognizable as designated bike paths but have no signage - if they had signage, they would be compulsory.
(Slightly off topic, but:) I don’t know it exactly, but I think the reason why non-compulsory bike paths exist at all in Germany - along with this
“footway, but cycling is allowed” sign
basically comes down to failed bicycle infrastructure planning and execution in the last decades: The sign above is generally put up in places where cyclists should not use the road but there is no bike path and it would be illegal to put up the shared bicycle- and footpath sign (i.e. make it compulsory) because the path is not broad enough.
Bike paths are generally not signed as compulsory when it would be illegal to make them compulsory due to minimum safety requirements such as minimum width or distance to parking cars not met. (Or in general bike paths that fell into disrepair)
It’s a bit the same as with the “advisory bike lanes”, which also exist in Germany and in a couple of other countries - not compulsory, because they do not suffice the minimum safety requirements, as above. (Funnily enough, the translation of the German name for these kind of bike lanes is “protection strip” 
)
Hence, there is a general heightened interest at least in the Germany community to map both the distinction between “shared bike- and footpath” and “footway, but cycling is allowed” as well as whether a bike path is signed as compulsory, as well as whether a bike lane is a real bike lane or (just) a “safety strip” to be able to highlight bicycle infrastructure that may on first look appear fine, but in reality is of worse quality.
Thanks for the clarification! It would be nice if the access=designated wiki page made this a bit more explicit 
Well, the wiki can be edited. It is certainly undisputed that sidewalks are designated for pedestrians, so I added something to that effect.
Well, the original intention of designated vs yes was: both means it’s allowed, but designated has a sign, or something else to explicitly allow the usage. So it came down to yes: implicitly allowed and designated: explicitly allowed.
A lot of people have since used both values for different things and started interpreting different meanings into both of these values. According to the tag’s original meaning, an unsigned sidewalk would be yes, and a signed one would be designated.
So yes, originally bicycle=designated meant bicycle: signed=yes
So yes, originally bicycle=designated meant bicycle: signed=yes
yes, but foot=designated was implied for sidewalks, it is because cycleways are not implicit.
You sure? I think, *=designated came with highway=path - The German translation always was “gewidmet” and not “ausgeschildert/signed” – so certainly sidewalks included. Some documentation always said: designation can be learned from signs or from construction.
You never been to Austria 
Legally, a sidewalk (Gehsteig) must not be signed, when it gets signed, it becomes a footway (Gehweg). Both are designated/gewidmet for pedestrian traffic only.
The German translation was not part of the proposal, and as with many English words, there are many possible translations, all with a (slightly) different meaning. The original definition from the proposal is:
as well as
I’m not saying it’s still used like this, but that was pretty much the original difference. The fact that every country has interpreted designated differently lead to a mixed meaning of both yes and designated. And that’s why it’s hard to document this properly in the Wiki 
But as for the original question, it doesn’t matter how it’s tagged, the question was rather, whether there’s a legal difference between shared use paths and footways with “access allowed”. I just wanted to clarify, why the wiki is doing such a bad job describing the difference between designated and yes.
There is, by the way, a legal difference in Germany on top of the ones mentioned: small electrical vehicles, like e-scooters, must use a cycleway, or a shared use path, if there is one, but must not drive on a footway, even if cycling is allowed there.
Eh, manche sagen, nur die blauen Schilder erfüllen das, die Absicht dass etwas für etwas Verwendung findet, manche sagen, fürs Fahrrad sind auch die grünen ausreichend, manche sagen fürs Zufußgehen a.k.a Spazieren/Wandern sind auch die gelben ausreichend für ein designated. (In Austrialien ist das nicht anders als in Austria.)
Wenn dem so ist, dann JA, in Österreich gibt es “designated for pedestrians but cyclists allowed”, und nicht nur das, sonder auch für “mofa|motorcycle|motorcar|&c” nicht nur allowed sondern auch designated Nur weil niemand einen highway=residential mit motorcar=designated versieht… In der Theorie heißt das nichts.
Lemme think… the actual access rights are always a combination of signs/markings/characteristics and law. Locals have to know the result of this combination for a particulart situation. OSM data users have to rely on tags to know what access to grant.
So, local users tag the result of signing/markings/characteristics to provide OSM-wide understood access types. That way, data users do not have to know all country-specific signs, characteristics and markings, AND the country-specific legislation, and still be able to render, query, select, list and route.
If a knowledgeble local mapper can see in situ which access rules apply, there is ground truth for mapping the access tags, informing the rest of the world of the actual situation.
Especially for country specific defaults which do not match the general OSM-wide defaults, it is important to tag them explicitly. For the country in question it would seem logical to NOT tag the local defaults, but OSM-based applications need them, or they will be in error for this exceptional country. And of course, every country is exceptional in its own way. Exceptional is the rule.