Success!
TLDR: It was (most likely) not the THP7312 chip's fault. It was caused by a not-well-seated connector in the camera head!
I replaced the THP7312, but I don't think I needed to, since it was initially behaving exactly the same as before.
However as I was testing the new THP7312 I noticed an extra error message that was there only when the camera was connected to the mainboard saying (I could have noticed this error message with the old THP7312 too, I just wasn't testing the UART output with the camera connected, which was my mistake):
thp7312_mipi 0-0060: 0xf001 read failed
That was weird, that register that it failed to read is clearly a thp7312 i2c register.
(We still don't have a datasheet but here there's some free software code that someone's been recently trying to add to the linux kernel: https://git.uk.ideasonboard.com/THine/linux/src/branch/epaul/v6.5-rc1/rc/thine/thp7312/drivers/media/i2c/thp7312.c#L73 , and f001 seems to be a CAMERA_STATUS register)
So if connecting the camera makes i2c inaccessible, one explanation would be that the same i2c bus goes to the camera too, and it gets screwed up somehow. So with my attention now directed to the camera head, I opened it and found the big connector half-unplugged. After plugging that back fully, everything works fine, and the firmware download retries and fails are also gone.
Opening up the camera head was a bit painful, I removed the screws from the ring light, I disconnected the ring light wires, I removed the two white pads from the front, where I found two screws, and I removed the other two screws as well from the camera head. And I also had to remove two screws to open up the first joint cover. Then I had to cut a cable strap that was tieing the cable to a metal piece, without cutting the actual cable, and then I had to massage the cable upwards a bit, so I could successfully extract the camera assembly from the front case. (This was the most painful part). Then removed 4 more screws to look at the back of the PCB, and there is where I found the half-disconnected big connector. Be careful, there's two metal inserts that act like nuts for the screws that were under the white pads, those can fall out easily, and also the white button used to set the ring light brightness can fall out. I re-seated the connector, and I added some tape to the big cable cause the joint started to tear up the insulation, and then I reassembled everything in the opposite order.
I wiki-fied some of the information I now know, in order to help people trying to repair the same device in the future: https://repair.wiki/w/EPSON_ELPDC21
@physicsonion I hope you have the same problem and my experience will help you too.