Delete volume, folder or file from Time Machine backup

I've noticed that my Time Machine keeps a previously existing volume in my backups. I no longer use that drive and to save 200+GB of Time Machine space I want to delete it from my backups.

I am not given a choice of deleting that specific volume from the backups using either Finder or within the Time Machine application. I can't delete a single folder or a file either.

This doesn't change although I login using an admin account.

This doesn't change after I reboot the machine.

I'm currently on macOS 11.6 Big Sur but I've had this problem or inability since version 11.2 at least.

The volume isn't present in my system, or even available to reconnect, so I can't go the route of excluding it in the Time Machine preferences.

Is there a preferences file where some settings are stored which are not presented by the GUI, maybe under ~/Library? I'm accustomed to editing xml files. I just need to know in what direction to look. Just hit me. :)

So much seems to have happened to Time Machine with macOS version 11. Unfortunately none of the guides I've found by googling applies to Big Sur and my issue.