I played around with both Go and Rust from Python and the garbage collection made things harder not easier. Now we write lots of Rust modules for Python and managing memory is pretty easy. We have Python wrapper objects that keep one pointer alive.

It sounds like you're mostly worried about memory leaks, but the primary concern with trying to get two separate GCs to play nicely isn't leaking memory, it's double-frees (both GCs trying to collect the same resource) and use-after-free (code in one language trying to use a resource that's been accidentally collected by the GC of the other language).

IE6 had exactly that issue, the DOM was implemented using COM which has its own GC (refcounting) separate from the regular JS runtime.

If you created a cycle between DOM and JS by, let's say, adding an event handler to a DOM node — thankfully that's something you'd never do when developing web pages & applications — you'd start leaking memory which would survive across page reloads.

There was actually a bit of software called Drip, it was just a webview wrapper (technically an MFC app with a browser COM component), you'd launch it, open your page, click the "blow memory" button and it'd reload the page over and over again listing elements which had survived between reloads.