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Does it save to the cloud so I can play on both?
Yes, and if you wind up moving to a console (once console versions come out) it will support those saves on console as well - if the launcher is to be believed.
Yup, I’ve tested windows->steam deck so far. No reason to believe it won’t work the other way around (paths seem to be compatible at least).
I can confirm that syncing through steam cloud works both ways. I also tried remote play while on the same network and I didn’t encounter any issues.