Just to provide some background on that, I think it was Sierra or High Sierra, Apple added a security feature for some obscure exploit. The security feature is sometimes referred to “app translocation”, when an app has a “quarantine” flag, instead of running from the folder you launched it from, it is moved to a read only disk with a random mount point path, somewhere inside /tmp.
Apps that appear inside the downloads folder gain a quarantine flag (not sure who assigns the flag).
The finder will remove the quarantine flag when you move the app outside of the download folder.
The read-only part is what makes the update mechanism complain, clearly that won’t work.
The wording of the updating error message is unfortunately also something we haven’t written, as it’s part of the updater library we use.
So the fix is to move Sparkle from Downloads to Applications. This doesn’t always work (the Finder sometimes misses removing the quarantine flag), but does most of the time.