I'm not sure if it's exactly what you're looking for, but I had a similar need and wrote this extension for my personal use: https://addons.mozilla.org/en-GB/firefox/addon/sihn/

It adds "parent" and "root" buttons under every comment. You can use the collapse button next to a post to get to its next sibling. (They are also made easier to hit on mobile.)

Firefox only though.

Floating buttons are…kind of annoying, to be honest. Just like those “back to top” buttons a lot of websites use.

I prefer the current option to hit the '-' to collapse threads when I'm done with them and not having any more click/touch targets on screen. It seems like the collapsing is remembered while logged in across devices and sessions.

Sync for Reddit allowed you to map volume buttons to thread up/down. That was super convenient and fast. Unfortunately, it seems Apple does not look to such features kindly.

I hope that HN doesn't add anything. It's great just the way it is.

People can certainly add whatever they want with browser extensions, though.