[backport#16908] test: mempool entry time is persisted

Summary:
Also, remove the now unused "Mine a single block to get out of IBD".
This was fixed in commit 1111aecbb5.

https://github.com/bitcoin/bitcoin/pull/16908/commits/1111170f2f0141084b5b4ed565b2f07eba48599a

Depends on D6522

Partial backport of PR16908

Test Plan:

test_runner.py mempool_persist

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D6523