First I made sure X was working the way I wanted with Intel graphics. There are a handful of ways to do hybrid graphics on Linux, depending on what you want to be able to do, and how old your hardware is (including "I didn't even want this thing, just keep it powered off forever"). The Arch wiki has some pretty good guides [1] that are helpful even if you're using a different system.
bbswitch seems to work on my system, and the interface is really simple [2]. But there's also this page on acpi_call [3], which suggests that bbswitch is old and unmaintained and that newer systems do something different. From a quick scan, it looks like the Arch wiki also mentions this approach.
As far as drivers go, I know everyone likes to dump on Nvidia for their closed source mess, but on every system I've used with Nvidia hardware (desktops and laptops), I've found that the Nvidia drivers have universally been more reliable than nouveau, so that's what I use.
[1] https://wiki.archlinux.org/title/hybrid_graphics (poke around in "Related Articles" too)
[2] https://github.com/Bumblebee-Project/bbswitch#turn-the-card-...
I have a friend who I convinced to buy a Thinkpad and stick ubuntu 20.04 on it. Unfortunately he got a more expensive X1 one with an Nvidia Graphics card, it strangely overheats when he needs to charge it and plugs it into the AC. I suspect the power settings are all over the place. I've not had chance to get a log from him yet. How did you "power down" your nvidia card?