Can I update my iOS back to 15.02

On my iPhone 12 after a week of update it is laggy, slow or no keyboard response, try to get into Apple Store and it says waiting to connect. I turn off WI-FI and try it cell same problem . Turned off cell and tried with WIFI same problem.

Do I need to go to Apple Store for a new Sim Card.

You can not downgrade iOS.

I want to update my iPhone back to 15.02

Apple does not support rolling back the OS version on iDevices.

No, you go to your service provider for a new SIM. Have you tried a forced restart?