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 ;)
How do I install the ad block extension on BAS?
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@robby-77 You are getting this error because you installed the extension directly from the chrome store.
You can fix this in 2 ways.
Method 1: Use the extension ID.

Method 2: Because you used the wrong link.
Please check again your extension link, I believe it will look like
https://chromewebstore.google.com/detail/ublock-origin/cjpalhdlnbpafiamejdnhcphjbkeiagm
But to install it, the link must look like this
https://chrome.google.com/webstore/detail/ublock-origin/cjpalhdlnbpafiamejdnhcphjbkeiagm -
@BAS-Viet-Nam Thank you so much