The only app that doesn't auto-update for me is Fdroid itself (ironically), because it targets an old Android version. Running Android 14 on a Pixel, so with the strongest Google fuckery.
Are you sure your Fdroid client is up to date? The new API was implemented in 1.19, and apparently I even misremembered and all you have to do to enable Fdroid to auto update its apps is to manually update them for one last time (so no fresh installation required).
Another long shot: there's an option to force the old installation method hidden in expert settings - maybe you could check if that isn't enabled?
Yeah, this seems properly configured. No clue why it isn't working for you.