CI lints analogous to `linera-protocol`

[ndr-ds]

It seems like we already build things with wasm-pack build --target web in CI, but even though we don't have a lot of Rust code, we should probably do something analogous to what we do in lint-cargo-clippy from linera-protocol.
There are several others, like lint-check-copyright-headers, lint-cargo-machete, lint-cargo-fmt, lint-cargo-sort, that we might want to consider doing something similar here as well.

One that I'm not sure is lint-check-for-outdated-readme, but it could make sense to have something similar if we decide to add a README specific to client-worker (which might not be a bad idea).

[Twey]

#16 covers Clippy, but the others are also potentially useful!