refactor(linux-client): replace client-tunnel with headless-client which is the same thing (#4516)

Unfortunately I had to keep `linux-client` to get the compatibility
tests to pass. #4578 aims to remove that package.

Please add to this list if you think of anything:

```[tasklist]
# Things that may break that CI/CD won't catch
- [ ] Github release artifacts
- [ ] Knowledge base 
- [ ] Docker images
- [ ] Docker containers
- [ ] Existing `linux-client` users
- [ ] Anything that downloads ghcr artifacts
- [ ] Nix (Not sure if it's built in CI. It had a merge conflict)
```

Refs #4515, and #3712, #3782

I think this is what Thomas and I agreed on in Slack / Github

---------

Signed-off-by: Reactor Scram <ReactorScram@users.noreply.github.com>
Co-authored-by: Thomas Eizinger <thomas@eizinger.io>

docs/README.md

@@ -97,7 +97,7 @@ product documentation, organized as follows:
     and deployed to your infrastructure.
   - [rust/relay](../rust/relay): Relay - STUN/TURN server to facilitate
     holepunching.
-  - [rust/linux-client](../rust/linux-client): Linux CLI client.
+  - [rust/headless-client](../rust/headless-client): Cross-platform CLI client.
   - [rust/gui-client](../rust/gui-client): Cross-platform GUI client.
 - [swift/](../swift/apple): macOS / iOS clients.
 - [kotlin/](../kotlin/android): Android / ChromeOS clients.