feat: migrate to async_nats client (#18165)

* feat: migrate to `async_nats` client

* fix: port nats-integration-tests to async_nats

* Bump async-nats to v0.28

* Bump to latest git revision

* cargo vdev build licenses

* Use 0.31.0 for now

* bump client_capacity to 1024

* Replace std::thread::sleep with tokio::time::sleep

* Revert "bump client_capacity to 1024"

This reverts commit 365d10a.

* Flush the connection before finishing NatsSink

* Flush subscribe before proceeding with the test

* Fix NATS NKey auth

Port to async-nats was using NKey public key when calling `with_nkey`.
It should use the `seed`, which will be used to generate key pair.

Signed-off-by: Tomasz Pietrek <tomasz@nats.io>

* Flush after every publish

* fmt

* downgrade time to 0.3.23

* cargo vdev build licenses

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Signed-off-by: Tomasz Pietrek <tomasz@nats.io>
Co-authored-by: Timur Makarchuk <timur.makarchuk@gmail.com>
Co-authored-by: Tomasz Pietrek <tomasz@nats.io>