When I run apt show foo I see in the output a line that says "Priority:" and one of the values:
Can I use the apt_preferences file to filter packages based on this value? For example, I would like to install "required", "important", and "standard" packages from debian stable, but "optional" and "extra" packages from testing.
No, apt_preferences doesn't permit filtering by package priority, only by name, version and origin (for several meanings of origin).
Mixing Debian releases wouldn't work anyway, because of dependencies. Many optional/extra packages in testing require more recent versions of required/important/standard packages than the ones in stable.
If you want to have a stable system and to be able to use some programs from testing, install stable and set up a schroot environment with testing. See How do I run 32-bit programs on a 64-bit Debian/Ubuntu?
