Starter staying engaged

1999 Toyota Camary had a no crank complaint. I checked battery voltage which was good and cleaned bat terminals. Engine started after a click or 2 but the starter stayed engaged with engine running. Turned off ignition but starter continued to stay engaged until I pulled battery terminals. I think there is a ignition switch concern that needs to be replaced but have not done any testing yet. Also wondering if I should replace the starter since its probably damaged as well. Any suggestions…Thanks

Most of the time I’ve seen a starter NOT disengaging is the gears on the starter or flywheel had a burh or was damaged. I suggest replacing the starter…not disengaging is an easy to kill a starter in very short order.