I unzipped the full Beta download from the link provided, extracted it and replaced all the existing files.
It shows as this version, 1.3.76 build 1.3.8063.11439
The the normal Update button produces the expected “No update available” message
And the Beta Update button produced a small download and install process that seemed to work OK but didnt produce any change to the version or build numbers.
The issue is that a standard install that’s been regularly updated was unable to update any further without the manual intervention, for me at least.