live_kit_client: Suppress `clippy::arc_with_non_send_sync` (#16298)

This PR suppresses the
[`clippy::arc_with_non_send_sync`](https://rust-lang.github.io/rust-clippy/master/index.html#/arc_with_non_send_sync),
as there were some warnings that would—only sometimes—show up when
running Clippy.

Release Notes:

- N/A