However, I see in the product specifications page of the console controllers that they also support PC.
And the PC controllers sometimes support some of the consoles.
The only real difference between controllers, from a technology perspective, is that is some of them support bluetooth/2.4 GHz.
So I have two questions:
If they are already cross-compatible, why even bother having different types?
How should I decide which type of controller I should buy? It should support PC, console-support is not essential.
Note: I am a novice in game controllers but aware of different network stacks.
Edit: Thanks for the amazing response! These are my key takeaways from all the comments
Hall-effect sensors are a must
Default console controllers usually have stick drift
If you need trackpad, take PS5
8bitdo is a reliable brand, as per multiple responses
Most controllers have good support on Linux. But haptic feedback can be a hit/miss as it can be platform/game dependent
There are various connectivity wireless standards. Dongles are the most reliable but you lose a USB port.
Keep track of handsize/comfort and button layout
PS controllers have excellent support on Linux/Steam
If you want wireless, one thing to be concerned about is the latency of the gamepad. https://gamepadla.com tests many controllers for their latency.
Personally, I've just gone with xbox with their PC dongle. I only like controllers with the sticks in the xbox/nintendo configuration and the latency is great with their dongle. I also like that it uses standard batteries so I just keep some rechargables at hand for when it runs out. On the downsides, there is no low battery indication on the controller, so occasionally it just dies in the middle of use.
I also use and recommend Xbox controllers. Although I wish I knew about these cool high end brands before I bought. I grew up in a time where all third party controllers were trash, and I carried that opinion for too long.
I read this thread and I saw 8bitdo recommended a lot and I've seen them recommended elsewhere. The hall effect sticks seem to be the gold standard.
My main issue with the Xbox controllers (mine are for Xbox one) is the d-pad. It's not terrible but it's not even as good as say a super Nintendo controller for fighting games and retro games in general.
8bitdo ultimate v2 via dongle is alright except it disconnects by itself every now and then and refuses to reconnect unless you walk right up to the dongle and try turning the controller on a few times.