You said in your OP that someone gave you this iMac.
Is there anything on the drive that youneed to save? (exists nowhere else, no backup, really important personal info or pictures, etc)
If not, just swap out the present internal hard drive with your new SSD.
Install Ventura on the new SSD.

Yes, you have a Fusion drive, which is actually two devices: a spinning hard drive, and an NVME card. They are joined together through software, but some files are on one device, some others are on the other device.
Your Fusion drive includes a 2TB hard drive, and an NVME card with 128GB. That's why you have the unusual 2.12 TB capacity.
You might consider removing that 128GB card, too. Not really too useful as an internal, with only 128GB of space, AND it may be where that backup error comes from. (It just makes the SSD more challenging to swap if you decide to remove the old SSD card, too. It's on the back of the logic board, which has to be completely removed to get at the old SSD slot.

I wonder if someone gave you this iMac, because they were already having intermittent problems.

It's probably not a coincidence that the system volume copied OK with 118.44GB, almost same as the SSD card capacity (128GB), but the data volume (which is, well, data added; personal files/pictures/documents/etc. That errors out.
So, something going on with the fusion drive. I suspect that one of the devices is failing.