Just noticed that the "LastVersion" file in the profile folder, as the name suggests, gets updated when the profile is opened with (another version of) BAS e.g. from 114.0.5735.91 to 117.0.5938.63. Therefore it's not suitable for our need to determine the original version of which a profile was created.
But at least can be said what was the latest BAS version that worked with it ;)
bablosoft has never mentioned the possibility of downloading any old versions of BAS. Change the versions in the link, older or newer versions may be available for download.
Premium BAS license holders have the ability to compile BAS with other parameters, including some earlier versions.
I have compiled versions since 22.6.9, but I'm too lazy to throw in the file share and drop the link.