Replace logic that waits for staged sessions to get ready in tests

Now that `pm install` has `--wait` flag that allows waiting for
staged sessions to get ready, we do not need tests to run while
loop for doing the same thing.

Bug: 141832432
Test: atest timezone_data_e2e_tests conscrypt_e2e_tests
Change-Id: Ib19e5f8f95fc48e52efa1650061741c4ca160b44
Merged-In: Ib19e5f8f95fc48e52efa1650061741c4ca160b44
3 files changed