There is already some data labels for toll, the most important things, toll yes/no or price are handled well it seems. An important thing for full handling of toll roads is what kind of booth it is, it can be entry, exit or passthrough (another way of naming this is closed: entry + exit and open: fixed fee at start of toll road). All of which should be handled differently partially at least for price calculation. For more information, the following video shows what it breaks and what it is used for https://www.youtube.com/watch?v=iRt9NebmZfA.
Adding a tag like toll_booth_type or instead of barrier:toll_booth add barrieir: toll_booth_entry, exit and _passthrough. If wanted, the default behavior can treat these three like the barrier tollbooth before. If clearer, the toll booth type seperately could add the neede information about the toll booth type.
I agree it would be useful to specify the type of booth (although it could be inferred from the topology). Generally, instead of toll_booth_type you can use just toll_booth, the type doesn’t add anything because you do not allude to the kind of type.
Around here (in Italy) there are also the kind of booths you mention, passthrough and entrance / exit, and there are few (at least one) routes where there is no barrier, you have to pay in advance indicating your number plate (but rest assured, the recognized number plates will only be used for the evaluation of toll payment, and not be used otherwise, of course, oh and maybe to find terrorists and extremely dangerous criminals).
Another detail: the toll_booths usually have several lanes, and there are different types of gates, some are called “telepass”, which is a service for remote payment, it requires a specific device and your entering and leaving of the toll area will be registered (and billed) automatically, the others usually require you to pick up a receipt at entering (to prove where you started) while for exiting, you have several options, “for cards” means you can only do electronic payment (or with specific prepaid cards, named “via card”), and there are gates where you can do both, electronic and cash payment, in 2 variations: unstaffed and with a real person that can help you. Some of these lanes are always the same, others can adjust dynamically (i.e. sometimes with staff, sometimes unstaffed, or can reverse the direction). Afaik we do not yet map these different lanes/gates.