MacBook Pro shuts down when trying to enter Safe Mode

Make sure to disconnect all external devices in case one of them may be causing a problem.

You did release the power button once you see "Loading Startup Options" appear? If not, then you are forcing a power off by continuing to hold the power button.

If you released the power button once "Loading Startup Options" appears and this occurs, then you will need to perform a DFU firmware Revive to see if that makes any difference since it resets the security enclave chip & system firmware.

If a "Revive" does not work, then you will need to go the extreme route and perform a DFU Firmware Restore which will also reset the internal SSD destroying all data on it as well as the other items for a "Revive". On an M-series Mac, the DFU Firmware Restore also pushes a clean copy of macOS onto the internal SSD.

How to revive or restore Mac firmware - Apple Support

These are your only options available before having the computer repaired by Apple or an Apple Authorized Service Provider.

Ok, thanks for clarifying things.

If the laptop is powered on...even if it isn't booting, you will first need to completely power off the laptop. I personally like to press the Caps Lock key so its LED is lit before I try to force the laptop to power off by holding the power button for 10 seconds. The Caps Lock LED will go out when the laptop is fully powered off. If the laptop is already powered off, then if you press the Caps Lock key it will power on the laptop. These more recent Macs are a pain because it is very hard to determine what state they are in at any moment when they are having problems.

Once the laptop is completely powered down, then you can press & hold the power button until you see the "Loading Startup Options...." appear on the screen. Then you can release the power button and it should continue to the Startup Options screen.

If you cannot reach the Startup Options screen, then you will need to try a DFU Firmware Revive after which you should be able to access the Startup Options screen if the hardware is Ok.