MacBook Pro has more free memory after Time Machine backup

This concerns a 14-inch MacBook M3 Pro (November 2023) running Sonoma 14.6.1. Last night I did two Time Machine backups, to separate external hard drives, as I periodically do in case one of them fails, which has happened to me before. I then moved some folders, with about 35 GB of files that I'd copied to other hard drives, into the trash can. I did not empty the trash.

At some point during these processes, the computer's 4 TB internal hard drive started indicating about 250 GB more free space than it had before (c. 550 GB, now c. 800 GB). I noticed this only after I dragged those folders into the trash, so it could have happened at any point after the first Time Machine backup. I did not restart the computer during the procedures I've just described, and it has been at least several days since it was last turned off/on.

Can running a Time Machine backup free up space like this?

I'd be grateful for any insights!