Apply the same contextlib.closing pattern accepted in #7493 to the nine
remaining library-side sqlite3.connect sites: SQLiteFlowPersistence
(init_db, save_state, load_state, save_pending_feedback,
load_pending_feedback, clear_pending_feedback) and SqliteProvider
(checkpoint, prune, from_checkpoint). The connection context manager
only commits or rolls back, so the connections survived in a reference
cycle and kept flow_states.db / checkpoint databases locked on Windows.
Also close the read-back connections in test_checkpoint.py, which made
its TemporaryDirectory cleanup fail on Windows for the same reason.
Add lifecycle and failure-path regression tests.
Co-authored-by: Vidit Ostwal <110953813+Vidit-Ostwal@users.noreply.github.com>
