@AnotherCat - thanks for doing all that. And don't forget to vote.
I just installed version 3.8, for some reason I got this message from the Windows Trusted (ahem) Installer
I've never seen one of them after a calibre install before now, but I think I can recall other people reporting it. But I chose to ignore it; as I always do, some programs seems to issue such messages on principle. The only things running were firefox and my file manager. WTI must have gotten discombobulated because of all the uninstalls/reinstalls of calibre 64 bit I've been doing - poor thing.
I'd already unpinned calibre from the task bar, so I let it launch from the installer - and I pinned that instance to the task bar.
In version 3.7 I was able to consistently induce the extra icon by doing a restart. However, with version 3.8 I can't. I put some load on cpu, memory, and storage (SSD and HDD where libraries are) made no difference, except calibre starts and restarts were a tad slower - but no second icon - so far.
Be interesting to see if AC and TdM see similar results.
BR