"the date of commencement of the first tenancy at that premises that was subject to an RPZ, or the date of commencement of the first tenancy at that premises after an absence of more than two years that was subject to an RPZ at its commencment"
That would be giving them a free choice to provide either the date of first registration or the date it re-appeared after an absence of two years without specifying which of the two they should provide. But you need to specify you want the latest of the two.
Regarding the idea of adding "that was subject to an RPZ at its commencment" you don't need to do that because the whole point of asking for this data about properties with an initial introduction to the rental market (or re-introduction after a more than 2 year absence) is that whether they were introduced to an area under RPZ restrictions or not, the landlord was at that initial introduction free to charge market rent. That's why these are the only entries on the register which can be reasonably thought to be indicative of market rent.
Also adding that to a request might invite a response that it is too onerous to provide the answers. It might also just confuse them.
Regarding:
"the latest date of when each property first appeared on the register, or reappeared after an absence of two years or more"
This is meant as a suggestion to be improved for clarity, but I think it's right.
Each property will have date it first appeared on the register. A small subset of them will also have a date they re-appeared on the register after an absence of two or more years.
The date that is relevant in trying to ascertain how relevant that property's rental price is to "market rent" is the latest of those two. I believe it is correct, but perhaps someone could reword it so it would be clearer to a reader.