Can I change which drive my swap memory uses?

Well nigh impossible and even if you could do it, you risk corrupting your system.

In your current setup with macOS on an external USB drive you are suboptimizing your system and your question implies that you already sense this is the case.

My suggestion is that you re-do your installation the way Apple intended macOS & apps to be installed ... put macOS and your apps back on your internal SSD and move your data to your external 1TB drive.

Even with a boatload of apps, a 500 GB internal SSD is plenty of space for macOS, all your apps and swap file space. For example, on my Mac (also a 5K 27"iMac) with macOS Catalina, Photoshop CC, CaptureOne Pro, PortraitProStudio, Screenflow, MS Office and numerous other apps, only 153GB is used; that leaves plenty of space for swap and other virtual memory.

I do not believe that can be done as the Operating System Controls this Function.

If the computer is running off an External Drive with a Fully Installed and Bootable Drive - that is where the Operating System will place the SWAP File, when the Operating System decides one is required.

Additionally, and specific to Big Sur macOS 11 and Monterey macOS 12, the Operating System resides in a Sealed and Read Only Volume that can not be opened by the User or “ Bad Actor “ Software.

You can you move your entire home folder, but you need to keep an additional admin user on the internal. You need to create one to move the home folder anyway. Change the name of your macOS user account and home folder - Apple Support

Many of the large library-based apps can be set up to store files somewhere else. So, it may not be completely necessary to move the home.

Moving your home folder is possible from a technical standpoint but is at minimum an "iffy" proposition, not least of which is because your home folder contains a hidden /Library folder that is actively used by the system and applications. I do not advise moving your home folder.

For that matter, I do not use my home folder to store any user data. I purposely save all user data to a second/external drive (including music, video & photo libraries). The only difficulty I have run into is that in Outlook 2016 and later, Microsoft has hard-coded mail storage to an arcane folder deep inside the user Library folder and no one has yet found a way to relocate the "Outlook Profiles" folder to another location or drive. It's a bummer. (However, if you use the Mac Mail app, you can relocate your mail folder to another drive by using a symbolic link and giving Mail full disk access.)

Good Work and Advise 👍

Rather than moving the entire home folder, it is safer to keep it in the internal, copy subfolders of it to the external and replace them with symlinks.