I don’t completely understand.
Why does normal shortcut open website without extensions? Does it open in private tab? And you have extensions disabled in private tabs?

there is a bridge, but some parts of the fediverse got very mad about it
https://github.com/snarfed/bridgy-fed/
https://fed.brid.gy/

OH REALLY?

heh, good one

Is this the “agile” development methodology that I heard so much about?

GotHub seems to display basic GitHub stuff decently well.
https://gh.whateveritworks.org/

so this is similar to LibRedirect?
https://github.com/libredirect/browser_extension
https://libredirect.github.io/
check out this list of privacy frontends and see if you can implement any of them in Predirect

Also, I see that you only handle one instance for redirect. Either the default instance or custom instance.
Consider implementing multiple instances. Here is list of instances that LibRedirect uses:
https://raw.githubusercontent.com/libredirect/instances/main/data.json
Here is a list of instances that Farside.link uses:
https://raw.githubusercontent.com/benbusby/farside/master/services-full.json

Both LibRedirect and Farside still have to deal with the rate-limiting problem with Youtube and Reddit and I assume other sites as well. Invidious instance or Teddit instance can be rate-limited, resulting in video not playing or post not showing up.
If your extension does not distribute user traffic across multiple instances, then I assume that your chosen instances will get hammered into ratelimit even faster than other instances.
So consider thinking about solution for this.
One of suggestions that I like is to allow user to provide an URL to a list of instances.
That way, someone or some automated system can periodically compose a list of instances and users can “subscribe” to that list.

Also some useful links:
https://github.com/digitalblossom/alternative-frontends
https://github.com/pluja/awesome-privacy#social-networks-and-platforms
https://github.com/mendel5/alternative-front-ends
https://matrix.to/#/#alternative-frontends:tchncs.de

reminds me of that joke from Futurama

Zapp:

You, ensign, whats your name?

Hugh Man sir!

Zapp:

Now that’s a name you can trust.

I was that age in 2006 and that style was strange to me back then as well