Extensions can't, correct but I wanted to bring up a special case regarding this

Isolated web apps a chrome feature for developing apps that run in chromium based on HTML (but tbh only really used in Chromebooks) do support raw TCP sockets so if this was ported to an IWA you could have Firefox on a Chromebook without an external server needed.

Chromium CEF could also embed the Puter proxy inside it too as a standalone application. No luck on Mobile though.