The only reason I went with SCART was because everything I was reading was saying SCART seemed to give the best RGB performance of all the different types. (RGB, Component, SVideo, SCART, etc.)

RGB is better than S-Video or composite video, yes, but RGB can be carried over various connector types: SCART, BNC, RCA, or DE-15, among others. Which connector you're using doesn't matter much; as long as it's carrying RGB signals, you're getting the best quality. (Technically BNC is the best connector for video quality, since it's coaxial and you can get them in 75 ohm impedence, which is ideal for video signals. But in practice it really doesn't make a difference at the low resolutions used by consoles.)

I've never really worked with any of them before, so I figured just turning everything into SCART, getting a SCART Switch, and just going with that would be the easiest way to go that gives the best quality.

SCART is "easiest" in the sense that SCART is the most commonly used connector for getting RGB from game consoles, so cables are readily available from several vendors. But, as you're finding out, the options for SCART switching equipment are actually very limited, especially if you care about getting something that's actually high quality. The Shinybow SB-5525 is actually the only SCART matrix switch that I'm aware of. Plus, SCART is just kind of annoying to deal with IMO, with its bulky angled connectors that like to work themselves loose from their sockets. But that's just my preference. If you'd still rather go with SCART, there's nothing wrong with that. Plenty of people get along fine with it.

Would you have any recommendations as to where to start researching what I would need for something like that?

Matrix switches are pretty straightforward. They have a bunch of inputs and a bunch of outputs, and you can control which input goes to which output(s).

The information on Extron's equipment specifically as it relates to game consoles is somewhat scattered, unfortunately. My Life In Gaming has talked about them a bit, RetroRGB has talked about them, there are a bunch of threads on the Shmups Forum about them. If you have questions, feel free to ask me and I can try to answer.

The main annoying thing about Extron's switches is dealing with audio. Not all Crosspoint/MVX units have audio switching, so make sure you're buying one that does. Extron likes to use 5-pin Phoenix connectors for audio, so you'll need some adapters to go from that to 3.5mm audio jacks (or RCA connectors, if you prefer). The adapters for inputs and outputs are different, so pay attention to that as well.

Since the RetroTINK-5X doesn't have a DE-15 input (the RetroTINK-4K will, thankfully!) or BNC inputs, you'll still need to adapt the output from your switch to SCART. You can use one of these for example, or this, or a custom cable (Retro Access should be able to make you one, or Wookiewin on eBay for BNC; be sure to specify that it's for DE-15/BNC input to SCART output, since SCART is directional). Adapting BNC to DE-15 or vice versa is easy, so any of those solutions will work regardless of whether you get a Crosspoint or an MVX.

Is there a big difference between Extron Crosspoint and MVX.

They're essentially the same, the only difference is that Crosspoints use BNC and MVXes use DE-15. I like the MVX because it's a lot more compact. Also, some MVX units have 3.5mm jacks for audio inputs, which is nice, though the outputs are still Phoenix.