You can move it, but your experience may be less than stellar. While it worked ok in the past, since Sonoma, people have experienced many problems.
You also must keep an admin-capable user on the internal SSD because the attachment to your external drive will break when it is not available at login.
There are better ways to accomplish what you want. All of the large storage Libraries can be set to exist on the external drive, Photos, Movies, TV, Music, etc. Mail cannot be set to exist on another drive.
If you wish to move your home folder,
Erase and format the drive APFS. You must enable permissions on the external drive by turning off "Ignore Ownership…" checkbox in Get Info. Create a folder on the drive to hold the new home folder. Maybe even Add another APFS volume to the drive in Disk Utility to use as the Home folder storage area. You could then just Ignore Ownership on that Volume.
Copy your current home folder to the external drive.
See this article on changing user name. Follow all the instructions precisely. If you fail to create a new admin user and log out of the user you are changing, you will lock yourself out of your Mac. When you get to the part about renaming the home folder, set its full path, e.g., /Volumes/MyNewHomeDriveFolder/shortusername. You don't need to change the short user name, just the path to the new home folder.