I was gonna say the RP3+ sounds like what you want, since you've the got the steam deck for when you need more power.
Emulation on Android
isnt the RP3+ a bit under powered for PS2 emulation? Im pretty sure most games are not playable unless you underclock/hack/downscale. Also, they are mostly just android devices, you are still have the 'screen control only apps problem, thou they might streamline how to configure and link screen positons to buttons
From the videos I've seen online, the RP3+ does have a native app you can slide in from the right to map buttons on the screen per app I believe.
I have and love an RP3+.
But I'd probably lean toward an Odin if you're willing to pay the extra money. The Snapdragon CPU is much more powerful, and will have more support for stuff like low latency Bluetooth codecs.
This is from a pure specs perspective, though. Someone else who's actually used an Odin might say that the controls suck.