I assume because I can’t find any cores for the PS2 in the online updater that there is no support for PS2 on Android. Do I have that right? (This is the Snapdragon 8 gen 2 on the Odin 2 so it’s not entirely crazy to ask a silly question. 
)
Edit: The reason I ask is because it would make syncing saves between the Odin and the PC a whole lot easier.
Correct. The only Android-compatible versions of PCSX2 are DamonPS2 and AetherSX2, both of which are closed-source forks that add ARM dynarecs (and crappy ads) to PCSX2.
There is the Play! core, which should be available for Android if you enable listing “experimental” cores, but it’s not super-usable. Many games have game-breaking bugs and the ones that don’t are still very slow to the point of not really being playable on most hardware.
No worries. The effort is to simplify rather than complexify and it sounds like the state of things is pretty complicated. I’m using the last Aether standalone verion (3668) before the dev dropped the project. Someday someone will pick up the torch.
There’s apparently been some work done on it, but nobody has access to the source code, so they’re limited in what they can do.
PCSX2 is open source, correct? So someone would have to design a great deal from scratch, but not all the way from a white sheet.
correct, it’s really the dynarecs that are a problem. Unfortunately, writing them is a very specific skillset that is not very common.