Check out Shuttle. If you want a hands-on project to pick up a framework, the Christmas code hunt is pretty fast (assuming the local crate makes it work after the fact?). I used it to switch from Rocket to Axum.
Manning has a book about Rust servers that might also be useful.
As for templating, if you know one template DSL, you should be able to pick up any of the others. I haven’t heard of Tera; it looks solid. Rocket supports it and Handlebars.
I think you’re finding a dearth of Rust servers hosting static content because, for the most part, the paradigm has shifted to static sites or SPAs hitting an API. That’s a personal observation not necessarily a fact. Any Rust server should be able to return static content.