Only few isolated parts were integrated into Firefox, everything else was simply thrown away and abandoned, and IMO it was for a good reason.
I've been programming in Rust for 5 years and I could barely understand the code in their repo. Not because it was somehow advanced but because it didn't make any sense. It felt like that with every decision they could make, they always chose the hardest way.
On the other hand, I have never done any C++ (besides few tutorials) in my life and yet I found both Serenity/Ladybird and also WebKit to be very readable and understandable.
BTW: If anyone wants to reply that Rust is different then yes, of course it is - but that's the point, if there is a language that maps nicely to your problem domain, it's also very fast, and well-understood then why the hell you'd use a language that is well-known to NOT map to OOP?