UPDATE - got annoying on the week I had to work with another salesforce site, it doesn't respect container boundaries either.

I ended up writing a brand new extension - Sticky TabSZ - to solve what was missing here.

UPDATE - Has not configuration and thus too aggressive - this "steals" focus from other sites that use salesforce as a backend upon authentication.

I liked the functionality so much that I created an extension that can be configured.
It's pending review here in Mozilla, but code is up for testing locksmizth/sticky-tabsz @GH

Original review:
Works as advertises - it will RELOAD the page you have opened, which is the desired action I was looking for.

I can confirm it works with Zen Essential pinned tab as well.
Sanity restored.

It kinda does what it needs to do, but there should be an option to limit what domains it pulls links from.

For example, if you're on both Legacy and Lighting instances of SF, it will try to load the Legacy links into Lighting which won't work.

Or if you have an integration between Confluence and Salesforce, this extension will go crazy by closing your Confluence tab, and then open a .png file in what would be your Lightning tab.

As it is, the implementation is too aggressive and makes it unusable in these common scenarios.