Other similar projects are using WebKitGTK, or indeed Electron: https://vieb.dev/ - again, probably not better/worse than QtWebEngine, just a different set of problems.
qutebrowser actually has an abstraction layer over the backend (which is why it can support QtWebEngine and the older/outdated QtWebKit, with little effort needed to keep support for the latter). If there is some new kind of library appearing some day which can draw to a Qt window and used from Python, it'd totally be possible to add support for it to qutebrowser without too much effort.
I had hoped for Servo to fill that gap at some point, but so far that hasn't happened yet: https://github.com/servo/servo/issues/27579
Another possibility is for Geckoview to be ported to Desktop platforms some day: https://mozilla.github.io/geckoview/ - something the people behind Tridactyl would like to happen: https://tridactyl.xyz/ideas/#port-geckoview-to-x86_64
As for extensions - other replies to your comment already mention this, but the main problem is that the WebExtension API is very constrained. On top of that, there's no API for handling keyboard input, so those extensions work by injecting JavaScript code handling keyboard inputs into every page you visit. That works, but only barely - lots of hacks are required for those kind of WebExtension limitations, and they won't work on pages where Mozilla decides extensions can't inject JS (such as internal pages or the Mozilla addons page). Again the folks behind Tridactyl have some ideas on how to improve the situation, but so far this hasn't happened yet: https://tridactyl.xyz/ideas/#write-a-keyboard-api-for-firefo...