Right now, we're using Docusaurus, which has been working well: https://github.com/celest-dev/website
Though, Flutter Web has come a long ways recently, especially with the WASM work that's underway [1][2]. Flutter is very well positioned, I think, for web applications requiring a lot of interactivity and complex layouts--the DX is phenomenal. For static sites, it's very hard to beat a pure HTML/CSS/JS stack in terms of speed and optimization potential.
That being said, I think there's a good chance we'll see more work on Dart web frameworks going forward. Projects like Zap[3] and Jaspr[4] and doing great work in this area already. And it's safe to say we may see a Celest Web framework one day!
[2] https://flutterweb-wasm.web.app