Idk about the latter, but Stardew Valley you can get from GOG or Steam for a pretty reasonable price, and it runs natively on Linux. You can transfer your save files between Windows, MacOS, Linux and Android for SDV, at least. If the second one you mentioned doesn’t have a native Linux version it should run through Steam through Proton. The website protondb can be used to find game compatibility.
Everyone is recommending KDE, but forgive me if I’m missing something, I don’t see it needing to be KDE support as a requirement on your list?
Any mainstream GNOME distro, eg Fedora, will have all the features you need through extensions (compiz window effect, gconnect for KDE Konnect, GNOME has the search you want by default and supports lots of customisation via shell themes, GTK themes, icon packs and extensions.
Edit: )