I’m looking into Rust GUI libraries myself and playing around with Slint. I think it can use QT as a renderer, but I could be wrong.
Out of curiosity, any specific reason for QT as a requirement? It’s certainly a good framework but I’m just wondering if there is anything specific for your use case.
Check out ForgeFed which is built on ActivityPub.
Forgejo is implementing support but I don’t know how far along it is.