Replace @async mentions in manual with Threads.@spawn

[Satvik]

According to #50356, @async is no longer recommended and new code should use Threads.@spawn. However, the manual still mentions @async in several places. This PR updates the user-visible mentions of @async to Threads.@spawn. I made sure to make docs locally afterwards and check that the references were updated.

Note: I'm not experienced with open source, so please let me know how I could clean up this PR or do things better. I tried to follow the contributing guidelines as closely as possible but it's likely I missed something.

[giordano]

Tangentially related issue: @sync is just barely documented #49921, it'd be nice to address also that one, while this part of the documentation is being revised.

[Satvik]

Tangentially related issue: @sync is just barely documented #49921, it'd be nice to address also that one, while this part of the documentation is being revised.

Would it make sense to merge the multi-threading and asynchronous programming pages at this point? Tasks seem to be the main way to do either at this point, and single-threaded asynchronous programming is now basically a special case of the parallel + concurrent model (if I understand correctly). Alternatively, it could make sense to refactor them into a "how to" page focused on Tasks, and a lower-level details page focused on Atomics, Threadpools, etc.

I could take a stab at it if there's interest.

[LilithHafner]

Thank you for your contribution! This PR looks great.

@giordano, documenting @sync better would be another good improvement, but does not block merging this PR now.