If the libraries needed to bring up a file chooser to export the save doesn't exist, your only option (outside of cloud saves) is to manually back up copies of saves.sol in ~/.local/share/Fancy Fish Games/Aground/aground
I came up with a workaround (though it needs a Windows or Mac computer). After copying the saves.sol file to a Windows or Mac computer that has Aground, I can export the files from there. (I have a network drive as well so it wouldn't be much hassle to do.) Since this is one of the only games I come back to from time to time nowadays (due to its unique gameplay style), I do end up exporting and importing these saves a lot. But thanks!