The biggest external SSD I can find is only 4 TB. I did find an external M.2 RAID that supports up to 32 TB. Technically speaking, those are “a fraction” of the price that Apple charges. But that “fraction” is about 80%. You aren’t saving that much money. Plus, your “super fast” SSD is going to be, at best, 25-50% the speed of Apple’s internal. You make up the difference with hassles like this and flaky USB bus. I would be shocked if you were using Thunderbolt.
Anyway, that link that Barney-15E posted is what you want to follow. It tells you where to set the location of your home directory. That’s the key part. You have to make sure to have a normal, admin user setup with the home directory on the internal. Log out of your user and log in to this failsafe user to make those changes. Plus, when your external flakes out, you’ll still have this failsafe to log in with and hopefully recover your data.
Don’t make any symbolic links. Just set the home directory. That’s the UNIX way. You will have to make sure to format the external as APFS. And make sure to enable ownership on the volume. Otherwise, certain flaky 3rd party tools won’t work. While logged out, and logged in to your failsafe, copy your home directory to the external. Then change the home directory. Then you can log in to the new user.
Enjoy your top-of-the line, half speed computer.