Adding my work folder to Macintosh HD

Starting in macOS Catalina, you cannot write to Macintosh HD since it's read-only:

About the read-only system volume in macOS Catalina or later - Apple Support.

In macOS Big Sur 11 and later, it's taken a step further when a read-only signed system volume (SSV) is used:

• Signed system volume security in iOS, iPadOS, and macOS - Apple Support
• What is a signed system volume? - Apple Support

Again, this translates to you can't place files directly on the Macintosh HD disk. However, you can put files anywhere in your Users folder (Macintosh HD > Users > your account).

but that makes it difficult to backup to Time Machine without including other huge files which I don't want to archive. Is there a relatively simple way of resolving this problem, assuming it's okay to do so?

Time Machine backs up everything on your Mac. Are you saying you don't want Time Machine to backup a specific folder(s) on your Mac? If so, Exclude files from a Time Machine backup on Mac - Apple Support.

Jack

You don't have to create the folder on your Desktop. You can put it anywhere in your user home folder. You just cannot create a folder at the root level of Macintosh HD.