Since `project` is created with `let_it_be`, state set via assignment or
could persist across examples in the spec.

To fix the problem, we do a combination of two things:

1. `let_it_be_with_refind` to ensure state resets between tests on
   objects that are modified
2. make changes on `build.project` instead of `project` in case they are
   different instances of the same underlying record

See #467641