How do I clean up 'Other' from my SSD in Big Sur.

See used and available storage space on your Mac

• Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

That is the hard truth and final word from Apple on managing the " Other " Category

The Other category are those files that the operating system manages, and you don't. See my post from this morning.

You can put most of your files on external SSDs and leave only the barest of documents on the internal SSD along with the system. Here's another take on the "Other" category.

The Other category is a potpourri of files which can include:

• System temporary files

• macOS system folders

• Archives and disk images (.zip, .iso, etc. - often found in the Downloads folder)

• Personal user data

• Files from the user’s library (Application Support, iCloud files, screensavers, etc.)

• Cache files: browser, Mail

• Mail messages & attachments

• Fonts, plugins, extensions

• Safari reading list

• iTunes backups

• Crud resulting from jailbreaking your iDevice

• Game data

• Saved data files

• Call history

• Notes

• Media

• Voice memos

• Other files that are not recognized by a Spotlight search

• Media files that cannot be classified by Spotlight as a media file because they are located inside of a package

• Files created and modified by other user accounts on your Mac.

They can be located anywhere on your hard drive.

The files that you have control over are located in the Documents, Downloads, Pictures, Music and Movies folders.  You can use either of these two free apps, GrandPerspective  or OmniDiscSweeper, to find the largest files on your drive so you can determine if they can be deleted or moved to an external HD for storage.  

Note: you can empty the Downloads folder after the apps and/or updates that were downloaded have been installed or applied.  Many users have found a couple of Gigabytes of files in their Downloads folder which are no longer needed. 

As for external SSD I'm partial to those from OWC (MacSales.com):

The drives from OWC (MacSales.com) have proven reliability, excellent customer support and warranties.  Consider one of these depending on your budget and needs:

Envoy Pro EX with USB-C or USB 3 - best SSD from a speed vs price standpoint

OWC Envoy Pro EX with Thunderbolt 3 - fastest if you have a Thunderbolt 3 port but more expensive and good if you're booting from it.

OWC Mercury Elite Pro 7200 RPM Storage - excellent choice for Time Machine usage, inexpensive and come in larger sizes that SSDs don't. Drives for Time Machine should be about 2 ½ to 3 times the size of the drive(s) you're backing up. 

Give OWC's Customer Support a call and see which they thing would best suit your needs for what you want to use them for.