Remove `actions-rs` from CI

[squell]

Our CI uses actions-rs. I think those can be replaced by simple run: invocations; especially seeing that actions-rs is no longer maintained.

There's also some other third-party actions being used where I wonder if we really need them:

• Swatinem/rust-cache
• awalsh128/cache-apt-pkgs-action; i think we introduced that one since a naked apt-get was sometimes not working.
• taiki-e/install-action; can't we just use cargo install there?

[rnijveld]

We should remove actions-rs, given its been unmaintained for several years now already. The rust-cache action makes caching Rust code compilation way easier, I would keep that. The apt one caches installation of apt packages, that speeds it up a whole bunch. And the install-action uses precompiled binaries, so that also saves a lot of time.