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.
Firefox and Chrome already contain significant amounts of Rust code, and the proportion is increasing.
https://github.com/chromium/chromium : C++ 74.0%, Java 8.8%, Objective-C++ 4.8%, TypeScript 4.2%, HTML 2.5%, Python 2.4%, Other 3.3%
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?
According to https://4e6.github.io/firefox-lang-stats/, 12%.
I would love an updated version of https://docs.google.com/spreadsheets/d/1flUGg6Ut4bjtyWdyH_9e... (which stops in 2020).
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.