Apple M3 Mac will not shut down

If necessary you can always force a shut down

force quit a shutdown by holding the power button/TouchID for ~6-10 sec.

Log out, sleep, wake, restart or shut down your Mac

Shut down or restart your Mac - Apple Support

To trouble shoot further you can:

—A SafeBoot Start up your Mac in safe mode - Apple Support will sort many anomalies

Does a quick disk repair before it fully boots up, and certain system caches get cleared and rebuilt, third party system modifications and system accelerations are disabled temporarily.

Login and test. Reboot as normal and test. Caches get rebuilt automatically.

This test will tell you if third party interference; most extensions etc are not loaded in safe boot mode.

—Test issue in another user (or guest user) account Change Users & Groups settings on Mac - Apple Support

This will tell you if it a universal issue or isolated to your user/admin account. 

*** (if you are using a wireless keyboard with rechargeable batteries— connect the charging cable, this will make the wired keyboard successful Safe Boot your Mac.)

unplug all non-essential peripherals when testing

Uninstall all third party apps that are Cleaners/Optimizers/VPN/Anti-Virus

all known to cause issues on the macOS

Why not? What happens when you try?

There's not enough information here to troubleshoot.