Simplify livekit config so that cargo check Just Works (#21661)

Supersedes https://github.com/zed-industries/zed/pull/21653

This enables us to use `cargo test -p workspace` on macOS and Linux.

Note that the line diffs in `shared_screen.rs` are spurious, I just
re-ordered the `macos` and `cross-platform` modules to match the order
in the call crate.

Release Notes:

- N/A

script/check-rust-livekit-macos

@@ -0,0 +1,19 @@
+#!/bin/bash
+
+
+set -exuo pipefail
+
+git apply script/patches/use-cross-platform-livekit.patch
+
+# Re-enable error skipping for this check, so that we can unapply the patch
+set +e
+
+cargo check -p workspace
+exit_code=$?
+
+# Disable error skipping again
+set -e
+
+git apply -R script/patches/use-cross-platform-livekit.patch
+
+exit "$exit_code"