Use recommended NATS.Net client for Nats package

[Alirexaa]

What this PR does / why we need it:
This pull request introduces several significant changes to the NATS health check implementation. The updates include replacing the NATS.Client package with NATS.Net, refactoring the NatsHealthCheck class to use the new client, and updating the health check registration and tests accordingly.

Dependency updates:

• Replaced NATS.Client package with NATS.Net package in project files and updated the relevant using directives. [1] [2] [3] [4]

Code refactoring:

• Refactored NatsHealthCheck class to use INatsConnection from NATS.Client.Core and simplified the health check logic.
• Removed NatsOptions class, as it is no longer needed with the new NATS.Net client.

Health check registration:

• Updated NatsHealthCheckBuilderExtensions to support a client factory for creating INatsConnection instances and simplified the method signatures.

Tests:

• Updated unit tests and functional tests to use the new NATS.Net client and modified the test cases to reflect the changes in the health check registration and implementation. [1] [2]
  Which issue(s) this PR fixes:

Please reference the issue this PR will close: #[issue number]

Special notes for your reviewer:

It's recommended to use NATS.Net for .NET 6 upwards.
Also, we use the same approach (#2040) to register client singleton.

Also, this PR should fix #2199

Does this PR introduce a user-facing change?:

Yes. NATS.Client removed. All previews AddNats were removed and a new one using the factory method was introduced.

Please make sure you've completed the relevant tasks for this PR, out of the following list:

• Code compiles correctly
• Created/updated tests
• Unit tests passing
• End-to-end tests passing
• Extended the documentation (Readme should be updated after approval)
• Provided sample for the feature

[adamsitnik]

The changes look good, I've added some ideas for minor improvements. Thank you @Alirexaa !

BTW is there any chance you could find some time to add a README.md and use NATS.Extensions.Microsoft.DependencyInjection in the code sample? We do sth similar for Npgsql: https://github.com/Xabaril/AspNetCore.Diagnostics.HealthChecks/tree/master/src/HealthChecks.NpgSql#recommended-approach

And it would be nice to describe the breaking change in the README as well

[adamsitnik]

nit: some of our users may be searching for the samples in our test project. This code is valid, but it registers a factory that is going to create a new connection instance every time a health check is going to be invoked (which may lead to resource leaks etc).

Would you have some time to use NATS.Extensions.Microsoft.DependencyInjection instead and just call AddNatsClient from that package?

Here I've found some samples (in a test project ;)): https://github.com/nats-io/nats.net/blob/3f919ddcd55ea0f765b4ce9b4137e2a58c589683/tests/NATS.Extensions.Microsoft.DependencyInjection.Tests/NatsHostingExtensionsTests.cs#L73

[Alirexaa]

I did not use AddNatsClient in this test because I wanted to test the client factory.
But you are right. It may lead to resource leaks. So, I kept the client factory but changed it to return the created client, not to create a new one.

[adamsitnik]

LGTM, thank you very much for your contribution @Alirexaa !