Most OEMs usually show an update screen on their radio, even if something unrelated is being updated.

If the update is taking a long time it could be a really big file on a SOC. It could also be a smaller file being written to… very slow internal memory because when the part was sourced 8 years ago no one considered including memory read/write speed in the sourcing documentation. I’m betting the second, unless this OEM didn’t include background programming on SOCs, which is kind of foolish given how much easier it is on a SOC than MCU.

I can’t speak for this particular OEM, but 12 volt lead acid batteries don’t have very deep power reserves. The OEM choosing to leave the battery on during programming is likely a method of ensuring there’s enough juice to install the update and start the car on the next attempt.