Set the default log_level to info in all tests

This is a follow-up to 116de07. That change was for two reasons: 1) speed up the
tests by reducing the amount of log lines 2) avoid a deprecation warning from
a6de6f5.

This setting need to be on the basic app too, otherwise the deprecation warning
will show up on other unrelated test cases.
Set the test_order in the basic app as well, see 58e8b48

This removes the unwanted deprecation warnings in the tests
Added tests for log_level deprecation

Closes #17756

[Godfrey Chan, Zachary Scott]