SET TRANSACTION SNAPSHOT sounds like replicated environment but isn't

The following documentation comment has been logged on the website:

Page: https://www.postgresql.org/docs/14/sql-set-transaction.html
Description:

Hello,

the wording on the SET TRANSACTION SNAPSHOT left me a bit confused. It says
"To begin a new transaction with the same snapshot as an already existing
transaction" and it feels like basically taking over an existing
session/transaction or being able to replicate a transaction from that
snapshot on. But I found that a temporary table created in Session 1 with
transaction A is not available from Session 2 with transaction B with
snapshot taken over from transaction A. I guess "obviously", as using the
snapshot does not give me the same permissions as the original transaction
starter so I can't replicate everything that Session 1 would have been able
to do in transaction A.

Also I couldn't find what the snapshot includes. Maybe it includes said
temporary table but the second session has no permissions to view it. Maybe
not. But I guess that's not actually important.

Maybe it is possible to add a sentence that starting from the snapshot of
another transaction does not include inheriting any permissions (or
temporary resources) on that snapshot. It's kinda obvious for different
users with different permission levels but especially the temporary table
case looks (at least with squinted eyes) like it could work.

All the best
Mario Wenzel