Grant Fritchey explains that Query Store data gets backed up like regular data, but with a caveat:
The core of the answer is very simple. Query Store, like any other data written to a database, whether a system table or a user table, is a logged operation. So, when you backup the database, you’re backing up Query Store data. When you backup the logs, you’re also backing up Query Store data. A point in time will include all the data written to the Query Store at that point.
However, that’s the kicker. At what point was the Query Store information written to disk?
Read on to learn when, and what you can do about it if you prefer otherwise.