Huh‽ While running with QtWebKit still happens to work, qutebrowser has supported QtWebEngine (based on Chromium) since 2016 or so, and it's been the default since v1.0.0 in 2017. If you're still using it with QtWebKit despite the warning being displayed about it, or using a heavily outdated qutebrowser version, that's on you and not qutebrowser...
If you're running an up-to-date Qt and qutebrowser, that'll currently be based on Chromium 122 from April 2024 (with security patches up to Chromium 131).
Ah, Verso looks nice and active, that wasn't on my radar. I kind of lost hope after a lot of embedding tracking issues and meta-issues over the years (the ones you linked is the third one I've subscribed to I think).
If you're running an up-to-date Qt and qutebrowser, that'll currently be based on Chromium 122 from April 2024 (with security patches up to Chromium 131).