If I open a folder in my file viewer (outside of RStudio) I see the .Rproj file and the .Rproj.user folder.
See point 2 in https://support.rstudio.com/hc/en-us/articles/200526207-Using-Projects "Creates a hidden directory (named .Rproj.user) where project-specific temporary files (e.g. auto-saved source documents, window-state, etc.) are stored. This directory is also automatically added to .Rbuildignore, .gitignore, etc. if required."
I was thinking, maybe that folder, or .Rhistory, might be causing problems (wild guess). I recommend trying deleting .Rproj.user and .Rhistory in a copy of your folder (especially as you don't have the safety of version control), and trying to open the .Rproj from there.
I think there's benefit in learning git even for internal stuff but that's a topic for later/another day of course!