Stallaris is supposed to have Steam Cloud, so the first step would be to go to

https://steamhost.cn/account/remotestorage

and check whether there are files for it.That way, you know whether your old computer isn't uploading, or whether your new computer isn't downloading and can fix the correct side.

I can't tell you what to do with saves you may have lost but going forward I thoroughly recommend you download GameSaveManager - it's saved my bacon many times over the years.

It makes it easy to collate and make it easy for you to back up saves for any games all in one.

I use it to store games I've played, and bung them onto a backup drive, so if things do go wrong, I can always revert.