Just FYI, I ran into the same issue today also on Windows 10 and I think I found part of the problem.
Checking the default install location at C:\Users\USERNAME\AppData\Local\itch I found that v25.5.1 had installed correctly, but v25.4.1 had failed to uninstall.
It was this older version of the app that Windows launched when I clicked on the Itch icon or searched for Itch from the Task Bar, so every time it launched it reported that v25.5.1 was available.
After deleting this old version, I am now able to launch the most recent version as expected.