Add more functional tests to non-blocking presubmit.

These tests have stabilized in postsubmit and since our functional tests
are only at INFO level (non-blocking) on presubmit, it's safe to include
them there too.

Bug: 384434389
Test: EXEMPT test change
Flag: EXEMPT test change
Change-Id: I1216f229d534394d8e563c2866a4e85f6852c5e0