Problem restoring iMac from Time Machine backup

Hello. I have a 2019 27-inch iMac with a 2TB Fusion Drive. Last week, my wife spilled coffee on the keyboard and the computer displayed a message "Your computer was shut down due to a problem." After she dried everything up, we couldn't get the computer to boot past the log on screen. We made an appointment for the Genius Bar at our local Apple store, and they ran diagnostics and said the hardware passed all tests, and recommended a complete wipe of the hard drive, reset to factory specs, and then restore the system from my Time Machine backup, which I have on an external hard drive. So we did that, but now when we start up the computer and try to import the Time Machine backup, I get a message saying there is not sufficient room on the computer to import the backup. The backup is 1.52TB in total, so there should be enough room. I had a chat session with Apple Support, they had me restart in Recovery Mode and use Disk Utility to re-erase the internal drives, reload Mac OS, and try again. The same message appeared - not enough space to import the backup. They also had me restart in Recovery Mode and try the import from the Utilities screen. When we did that, the most recent system backup it found was from 2021 - but when I first tried to import the backup earlier, (and every time I've tried outside of Recovery Mode) the most recent backup was from last week, the day before the coffee spill.

I'm hoping someone can point me in the right direction on how to restore my system from the backup. If it helps, here are the internal drives I see from Disk Utility:

Untited, APFS Volume, 120.88GB, 99.95 GB free

Untitled - Data, APFS Volume, 120.88GB, 99.95 GB free

Untitled, SATA Internal Physical Volume, Mac OS Extended (Journaled), 2TB, 2TB free

Untited - Data, APFS Volume, 120.88GB, 99.95 GB free

Thanks for any assistance.