I started using it a few days ago, but I've been under the impression that PDF has been possible in Typst since mid-2023 at least.
As of 0.4.0, Typst supports PDF, SVG and PNG outputs. The Typst team seem to be rapidly adding features, but I don't think HTML support is coming soon.
There is currently work done to support basic HTML support. PDF is supported since day one of the public release in march 2023 (before v0.1). The roadmap mentions tagged PDF which is mainly needed for accessibility.
As of 0.4.0, Typst supports PDF, SVG and PNG outputs. The Typst team seem to be rapidly adding features, but I don't think HTML support is coming soon.