I have a clean WordPress install using the Twenty Twenty-Two Version: 1.2 theme.
The only plugin installed is yours, 'Make Paths Relative'.
In settings I checked the box for 'Image Paths'.
Then changed the WordPress > Settings > General > Timezone from 'London' to 'Los Angeles'
Then BOOM! the following error appears:
One or more database tables are unavailable. The database may need to be repaired.
Upon investigation in myPHPAdmin we discovered that the _options table field 'option_name' > 'siteurl' and 'home' were blank where the websites url should be.
Once, we manually put in the URL into these fields, went back to the site, and refreshed; it worked again until we changed the timezone back again.
We also tested this on different web hosts, servers, and with different themes and were able to reproduce the behaviour.