When would two consecutive SELECT queries run in the same session produce different results?

The scenario you described would definitely work, although note you'd have to commit those changes (not sure id it was implied or not, but it's probably a good idea to be explicit).

Another idea that may or may not be a valid solution here is to play around with the ordering. E.g., consider a query like SELECT num_col FROM my_table. Since there is no order by clause, the database is free to return the rows in any way it chooses. Creating an index on num_col between the two queries would probably make the database prefer to query the data from it (full index scan vs full table scan), and chances are you'll get the result in a different order with and without the index.

EDIT:
Another idea could be if you query the current time (e.g., SELECT CURRENT_TIMESTAMP in PosgreSQL, other RDBMSs may have slightly different syntax) - no data in the database is changed, but consecutive calls to the same query will return different results as the time moves forward.

There is no need to assume that underlying data changes.

The simplest solution is using a volatile function. For instance, this might return different results when run at different times -- even with no changes to the underlying data:

select t.*
from t
where created_at < current_timestamp - interval '1 year';

Or:

select t.*
from t
order by random()
fetch first 100 rows only;

Actually, a query as simple as:

select random()

also meets the requirements, without actually having to involve any tables.

As you've said, the same two consecutive select would only produce different results if the data has changed between the two selects.

You could also have a select in a transaction where data was changed, and then have a rollback and to the same select and have different results but once again it implies the underlying data has changed.

If you set the With No Lock, you can query the same data two times and have different results, for example if a big update was running during one of you select. It's an edge case but it can happen.

Brent Ozark have very good explanation about the "With No Lock" issue https://www.brentozar.com/archive/2019/08/but-nolock-is-okay-when-the-data-isnt-changing-right/