Time Machine error - "There isn't enough space" message

I recently upgraded to Big Sur (late, I know) and keep getting the "There isn't enough space" error message when backing up to Time Machine on an external hard drive. I've erased and formatted the partition and keep getting the same message even though I'm starting fresh and there should be enough space on the hard drive. I used the same drive and partition on Catalina with no problems so the space should be there, at least I think so.

The estimated size of the backup is about 350 GB. MBP hard drive is 500 GB with 160 GB left. 500 GB partition on the external drive for Time Machine.

What am I missing here? Should I just extend the partition or is there some other trick to it?