Old Mozilla / Firefox with XUL / XPCOM[1] was probably about as close as you get. If you were willing to use the low-level interfaces, you could change just about anything as far as I can tell. But that led to security issues and issues with maintaining comparability when there was a need to change those low-level interfaces. So Firefox largely moved away from XPCOM and blocked extensions from calling XPCOM interfaces.

That said, AFAIK Pale Moon still allows use of XPCOM. And I think Seamonkey may be the closest remaining browser to the Mozilla of old. I believe you can still use all of the XUL/XPCOM stuff there, but don't quote me on that.

[1]: https://en.wikipedia.org/wiki/XPCOM

[2]: https://en.wikipedia.org/wiki/SeaMonkey

Interesting stuff - none of these seem to have that Smalltalk-like visual IDE bolted right into them.

Given how big and important a platform the modern web is - I really am starting to think - something like this should exist - where I have a neat little IDE bundled right within the browser using which I can evolve the browser...