For Chrome, I don't know if anyone has compiled the stats, but navigating from https://chromium.googlesource.com/chromium/src/+/refs/heads/... I see at least a bunch of vendored crates, so there's some use, which makes sense since in 2023 they announced that they would support it.
https://github.com/mozilla-firefox/firefox : JavaScript 28.9%, C++ 27.9%, HTML 21.8%, C 10.4%, Python 2.9%, Kotlin 2.7%, Other 5.4%
How significant?