Background: WT-17539 exposes set_key to the caller and removes auto-push; WT-17542 adds timestamp-based KEK selection at checkpoint. test/format currently exercises the key provider in pull mode only — the disagg.key_provider knob loads the extension at version 0 so get_key supplies all keys and the push path is never stressed.

Acceptance Criteria:

• Extend the disagg.key_provider knob (or add a dedicated knob) to select push mode (version 1), threading the choice through the shared disaggregated config in test/utility (TESTUTIL_DISAGG_INIT / disagg.c / test_util.h).
• Add a background key-rotation mechanism to test/format that calls set_key with a timestamp strictly above stable and above the previous push, on a periodic cadence, gated to the leader.
• A test/format run in push mode completes cleanly: the leader persists rotated keys, followers pick them up across failover, no set_key EINVAL or checkpoint assertion.
• Pull-mode and key-provider-off runs are unaffected.

Depends on WT-17539 and WT-17542.