iMac 2012 27“
13.0.1
Clean installation with 0.5.1, updated patches with 0.5.2
Have you got latest EFI firmware version?
Tockman is dead right to ask that question, it would pay to check this. The best way is to install SilentKnight 2.3, it's pretty much indispensable for keeping your unsupported Mac fully up to date IMO. You can get it from author Howard Oakley's site
here.
You might already know this so forgive me if you do, maybe someone else will get something useful out of it. Assuming your iMac late 2012 model is an iMac13,2, the last supported macOS version was Catalina. Catalina's last firmware update was shipped this year within Catalina 10.15.7 security update. Firmware version is 429.0.0.0.0 for my rMBP10,1, I don't know whether it can vary between Mac models. SilentKnight will do all that checking for you.
If your firmware is not up to date the workflow is this.
Install the last supported macOS, Catalina in this case, on an external drive (preferred), or on a separate partition / volume on the internal drive (more chance of instability but can work).
Added step:
There has been some discussion on the need to perform a PRAM/NVRAM reset before installing or updating the last supported macOS on the external drive / partition, so a reset is recommended. If you decide not to reset it, and your firmware does not update during the macOS install / update, try again, but do a PRAM/NVRAM reset before installing / reinstalling macOS
You then boot it, log in and go to system preferences > software update. Presumably if you already installed 10.15.7 it won't find any updates. If not, accept any updates it offers and update your Catalina drive / volume. It will download and install the Catalina 10.15.7 security update which contained the firmware update. On the last auto reboot, login and check whether the firmware updated.
Reboot into Ventura and check firmware version with SilentKnight, it should find your firmware is up to date.
Keep the Catalina external drive / partition handy just in case another Catalina security update hits before Apple discontinues support for Catalina. I believe that will be very soon, does anyone know?
Even if it does not fix all specific problems, at least you've eliminated the possibility that they were caused by old firmware.
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Edited, next day: After later discussion I've added a step to the workflow on performing a PRAM/NVRAM reset before booting into macOS to start the install / update process.