Zigbee smart door lock recommendation?

I want to check if there is a smart lock that checks all the requirements below:

  1. Support of Zigbee/Z2M
  2. Price is no more than $100
  3. Unlock with phsyical key
  4. No need to replace batteries every month
  5. NO CLOUD, local connectivity only
  6. Remote lock/unlock via HA
  7. Ability to set user codes with length 4-6 digits and set expiration time for these codes.