In principle it is possible that some packages may rely on configuration to pass their tests. If that configuration occurs via Preferences.jl, given that Preferences is path-based it seems likely to be necessary to find and copy the LocalPreferences.toml file to the new project directory.

I don't yet have a MWE, but I have a not-yet-public package that involves communication with a SQL database, and I handle the configuration of this interaction via Preferences. The package passes tests with Pkg.test() (following a custom line in my CI.yml file that generates the right LocalPreferences) but I have not found an incantation that works with TestEnv.