client: Use async connection in async TPU client (backport #25969)

[mergify]

This is an automatic backport of pull request #25969 done by Mergify.
Cherry-pick of 2436a2b has failed:

On branch mergify/bp/v1.10/pr-25969
Your branch is up to date with 'origin/v1.10'.

You are currently cherry-picking commit 2436a2bea.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	modified:   client/src/connection_cache.rs
	modified:   client/src/nonblocking/quic_client.rs
	modified:   client/src/nonblocking/tpu_connection.rs
	modified:   client/src/nonblocking/udp_client.rs
	modified:   client/src/quic_client.rs
	modified:   client/src/tpu_connection.rs
	modified:   client/src/udp_client.rs
	modified:   client/tests/quic_client.rs

Unmerged paths:
  (use "git add/rm <file>..." as appropriate to mark resolution)
	both modified:   Cargo.lock
	both modified:   client/Cargo.toml
	deleted by us:   client/src/nonblocking/tpu_client.rs

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/github/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

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[mergify]

automerge label removed due to a CI failure

[mergify]

automerge label removed due to a CI failure