I am aware that in Linux and MacOS environments updates are a more automated task and usually happen in the shell or CLI side of things... but I would just like to suggest this and collect the feedback on the possibility of this feature.
Mac diversion from me here. For CLI software, things are mostly managed by a package manager like homebrew, macports, fink, etc. But, for GUI apps (ignoring Mac App Store distributed apps), they commonly do their own version updating. A very popular technique is to use a similar kind of library to this one called Sparkle (https://sparkle-project.org). Though, it has update version check logic client-side, with just an RSS feed containing entries for app releases server-side.
Sparkle integration is something I've got on the list to look at with the Mac build. Basic integration into Inkscape is pretty simple when adding it to an Obj C app wrapper (the replacement for the <= 0.92.x Carbon wrapper). The tricky bit is getting it to integrate with a Inkscape preferences UI to set things like enable version checking, version check interval, enable beta release channel, etc.
If there's interest in doing a Windows self-updater, it'd be useful to discuss what would be desired for a preferences UI so we can work out a common UI for that, if possible.
Cheers, Tim