The other is a rack and pinion. That requires a gear on the servo and matching teeth on the rack. You can Google to see how to make them.Paul
Is there a possibility that you would need to open the lock from the outside when the Arduino / servo (or the power supply) has failed?...R
On the safety side, the latch bolt on the inside need to be made such that it is escapable incase of emergency. Perhaps make one side of the latch setup where it can be lifted/moved easily to un latch.
My plan is.. only planning now.. is something if a smoke or CO is detected, the doors unlocked and HVAC shuts off. It texts and calls.