Or even better IMO: a single "Install" button that autodetects the platform and does the right thing, with a little clickable arrow on the right side of that shows a dropdown with all available options for people who don't want the default (e.g. people on Linux downloading the Windows package for some reason).

Not only AppStream download button but other ones have all been redesigned to be visually uniform, less redundant, more familiar to users, and support l10n better, with this MR. You can see the discussion related to the MR here.

I have also tried to do a part of what @ngraham suggested: the topmost download button on an app page, on the right of the title, tries to be relevant to which system the user is using to browse, with this MR. Now it supports Android and Windows, because they are the other major platforms that our apps are available on. If the user is not detected to be on Android or Windows then the AppStream button is displayed.

So can we close this task?