Add integration tests for backup/restore workflow

[ethanhs]

This is to split out of #1761.

@BYK said the following:

the backup/restore dance is woefully undertested. I did some fixes and improvements there while writing the docs (it did not even work before that 😅). In the upgrade scenario, you may wanna add a backup/restore scenario too. That said it should only matter when there's a model/migration change.

This is part of the overall backup/restore improvement project for Q1 2024 (TBD)