fix: make `OutputWriter` references `Send` (#5931)
### Description
As I was hooking up the task cache I encountered the dreaded "future is
not `Send` as this value is used across an await" due to a
[`task_cache.restore_outputs(&mut
prefixed_ui).await`](https://github.com/vercel/turbo/blob/main/crates/turborepo-lib/src/run/cache.rs#L149)
call. The easy solution is to drop the `RefCell` and instead use a
`RwLock`.
[Quick reading that explains *why* locals that are held across an await
need to be
`Send`](https://blog.rust-lang.org/inside-rust/2019/10/11/AsyncAwait-Not-Send-Error-Improvements.html#how-are-async-functions-implemented)
### Testing Instructions
Added assertion to make sure we'll be able to hold `&mut OutputWriter`
across `.await` i.e. implements `Send`
Closes TURBO-1323
Co-authored-by: Chris Olszewski <Chris Olszewski>
