The operation can’t be completed because you don’t have the necessary permission.

Beginning with macOS 10.15 Catalina, you cannot modify anything files/folders outside of the "/Users" folder. The macOS system files located on the root of the drive are now on a protected read-only APFS volume (even an admin or root user is unable to modify items on the read-only system volume). See these Apple articles for information regarding the new drive layout starting with macOS 10.15+:

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

Signed system volume security in iOS, iPadOS, and macOS - Apple Support

The "Other" category are things controlled by macOS which macOS will release when it is ready and finished with those items. About the only item which may be included in this category may be the hidden APFS snapshots for Time Machine backups (or third party backup software) which theoretically can be thinned or deleted (do you really want to mess with the backups though?). These snapshots should be automatically deleted at some point after the backups have successfully transferred to external media (may be a day or possibly a week).

You need to delete or move your files from within your macOS home user folder to make enough room. The Downloads folder is a good place to start. I've heard people move their pictures to external media if they have a large collection. iPhone & iPad backups will be stored in the hidden Library within your home folder and can take a lot of room. Also make sure to empty the Trash after deleting items.

Even when deleting those large items, the data still may retained within the APFS backup snapshots until the backups have been transferred to external media. Sometimes even after this transfer, the snapshot may remain for a day or even a week (it is up to the backup software) and/or macOS. You may be able to thin or delete these APFS snapshots, but make sure the backup snapshots have already been transferred to the backup media.

View APFS snapshots in Disk Utility on Mac - Apple Support

https://derflounder.wordpress.com/2018/04/07/reclaiming-drive-space-by-thinning-apple-file-system-snapshot-backups/

If you copied large amounts of data to another folder on the boot drive, then that "copy" process did not actually make another physical copy of the data due to how the new APFS file system works....it just creates a simple link to the same (now shared) data. You must delete all links to the data before it is actually deleted (excepting snapshots mentioned previously).

The only other way to possibly delete "Other" is by just rebooting the Mac which may clear out some temp & cache files. Booting into Safe Mode will do a bit more (just reboot normally after booting Safe Mode).

Some Macs shipped with SSDs which are way too small except for just very basic computer use such as web browsing, video chats, or checking mail....those small SSDs were never made for storing data. Obviously your Mac doesn't have enough storage so you will either need to move your data temporarily to external media in order to upgrade macOS, or you will need to add some external media to store some of your larger files, or you will need to purchase another computer with more internal storage (just make sure to get enough internal storage since internal storage can no longer be upgraded on the latest Macs after purchase).

What is it, exactly, that you are trying to accomplish?

Writing an effective Apple Support Communities question - Apple Community

We cannot trust the Storage report as to where the usage really is, especially what “Other” or “system” is…

Are you implying you know the name it?