OP:
Where did this Mac come from?
Did you buy it with your own money?
Or... is it a "work computer", that was given to you by your employer?
As mentioned in replies above, if it came from your employer, it may have pre-installed company software/firmware on it (MDM?) which may prevent you from installing and running a copy of the OS on an external drive.
If the computer is actually YOURS, there probably isn't anything that can stop you from booting/running from an external drive "for work".
I would suggest using a USB3.1 gen2 drive for external booting.
You could also use thunderbolt, which is faster, but these drives are more expensive and many of them get HOT while running.
For an external USB3.1 gen2 SSD, you might consider either a Crucial X-9 or a Samsung t7 "shield" (or perhaps the new t9, if it's out yet?).
Remember to boot to recovery and go to the startup security pane and remove the "security" that prevents booting from an external drive.
Be aware that m-series Macs seem to be designed to run best when booted "internally", and that there may be glitches here or there when booting/running from an external drive. This doesn't mean you can't do it...