How can I tell the date of imagery? In Josm we have many choices. Most notable, ESRI* , is a different time than ESRI * (Clarity) Beta, which is newer?
It entirely depends on location (including adjacent areas in the same city), and sometimes on zoom (usually this goes away and is an artefact of tiles being updated).
For the most part you need to use local knowledge to determine which imagery is the most up-to-date in any area. Not all imagery has a time associated with it, and even then this may be a time based on composite imagery. In built-up areas changes to buildings (particularly new sub-divisions/housing estates) can be a useful hint: towns and cities seem to inevitably expand. It gets more complex when two sets of imagery are quite close in dates.
In my local area the two Maxar layers look identical. ESRI Clarity is several years old (it predates the development of a building under construction which was destroyed by fire in 2014), Mapbox is between the date of the fire and the re-development of the building in 2017. The Maxar imagery is clearly from summer 2018 when we had an extended drought, but in the ESRI Imagery layer grass is green. It is newer because the building work on the house 2 doors away has been completed. Bing is much higher quality and is leaf off (Winter/Autumn), but both pre-date the newest building work on the University campus. ESRI is newer in this area as houses have their roofs on, and as I collected addresses at least twice on that street this gives a rough idea of date. The ESRI imagery says it was captured on 3rd Sept 2019 (Ctlrl-B in iD0