If I got this right, you're using the Windows version of Stardew Valley in Linux, through Proton, right? If this is correct, the game won't look for the save files inside the ~/.config directory, because that's where the native Linux version puts them.

Personally I'd use the native version, and then install the mods manually. Because it's simply less work.

But if you still want to use the Windows version in Linux, you'll need to place your save files wherever Proton pretends that there's a Windows installation. Probably something like ~/.steam/steam/steamapps/compatdata/413150/pfx/drive_c/

If it is not in the directory above, you could create a save with some random farm name (say, "potatotree"), and then look for files called "potatotree". Then you'll know where the game "wants" the saves to be.

Can't speak to if it'll work in this instance. But if you make a new save and then overwrite that one with your actual save has worked for me in the past.

Note that there is negative reasons to use vortex with stardew valley. 90% of the mods are simple drag and drop into the mods folder, and the rest are drag and drop into the subfolder the xnb framework(?) Mod has for them.

I know I am forgetting something, but its been awhile since I played/modded stardew

Looks like you solved it but just for future reference, you can pull down Steam cloud saves manually from https://store.steampowered.com/account/remotestorage

Sorry if not relevant or you already found a fix. I've only tested one game in linux so far, Fallout Shelter (I mainly need VR to work and 2/3 of my VR library won't show in my list, yet), mine is on Kubuntu with steam from the steam page, not flat pak or whatever else as they won't work with VR at all. Did you have the save in the steam cloud? Cause when I did install Fallout shelter it brought in both my save games during install.