I have no idea what I did, I just opened the Excluded Folders menu to double check I wasn’t crazy and there was no way to remove them.
Don’t think I touched Obsidian much after that. Then the next day I open up the app (that’s been running in the background) and low and behold I have all my files! I no longer had any excluded folders, and all of them got resynced in the background. This is not what I desired, as I excluded them on purpose on this computer. I simply wished to unexclude one of them.
My best guess as to what I did was to tick and then untick one of the existing folders that I could see, and hit Done rather than exit out of the menu. The folders I had excluded were not showing in the Exclusion menu, as I had also deleted them afterwards, so perhaps they need to exist in order to either add or remove them? 
Either way, this is very unintuitive. I simply wish to get rid of some folders entirely on certain machines, due to them containing more sensitive information.