test: settings: functional: fix missing test_main

The functional tests for settings subsystem regressed with the
introduction of the weak test_main function. This was caused by
Issue #19582 since the common code was being linked as a library.

Update the logic of the common code to directly add the sources
to the `app` target. This resolved both Issue #19582 and #42396

Signed-off-by: Yuval Peress <peress@google.com>