So I tried playing Saints 2 with a switch controller connected and the game input just freaks out.
It seems like it runs all inputs at one time, is there a patch anyone knows of that fixes this?

do you mean you chracter is running in circles and / or control directions are entirely messed up?
this is a common issue with SR4, and sometimes 3. I have no knowledge of any fix.

No the controller sends all possible inputs to the game at one time, without any actual button presses from me.
The menu opens and closes the character jumps and moves randomly. It stops when I remove the controller.

pretty much the same thing (i also had this on a different install - same computer, same os, same gamepad).

sometimes it fixes itself. most of the time it doesnt.

Have you tried installing the Gentlemen of the Row mod? I'm not sure if it helps tbh, I didn't try my controllers without it. I added in the controller button prompt option and then installed the rest as default. I did have one issue where the main menu was scrolling uncontrollably, but that was while I was trying to stream using Moonlight and hasn't happened since. I did have to go remap all the controls to resemble a hybrid of the old GTA games and SR4 to not lose my mind, the default scheme is horrible.

But I'm using a 360 controller and an 8bitdo SN30 Pro in xbox 360 mode so I can't speak for how a switch controller will work with SR2 with any certainty, I know the Switch / Android native controllers operate a little differently than a DS4 or 360 controller. The later games had out of the box 360 controller support but SR2 seems to be generic, you might just need to calibrate it in Windows?

Sorry I can't be any more specific than that, but I hope something in there helps.