Improve rainbird device reliability by sending requests serially

[allenporter]

Proposed change

Update the rainbird coordinator to send requests serially, rather than in parallel.
Rainbird devices will often return a 503 to indicate the device is busy when it can't handle multiple requests at the same time, and we can see from device logs that it is likely to drop one of the requests when sending multiple at the same time.

This also simplifies some of the code to use newer APIs that are easier to use (the API now returns a set directly, rather than just having a method to check if an item is in the set). Also, one call previously was memoized in home assistant can now use memoization baked into the client (e.g. total number of stations, which does not change)

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New integration (thank you!)
• New feature (which adds functionality to an existing integration)
• Deprecation (breaking change to happen in the future)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Additional information

• This PR fixes or closes issue: fixes Rainbird failing #86134
• This PR is related to issue:
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
• Local tests pass. Your PR cannot be merged unless tests pass
• There is no commented out code in this PR.
• I have followed the development checklist
• The code has been formatted using Black (black --fast homeassistant tests)
• Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io

If the code communicates with devices, web services, or third-party tools:

• The manifest file has all fields filled out correctly.
  Updated and included derived files by running: python3 -m script.hassfest.
• New or updated dependencies have been added to requirements_all.txt.
  Updated by running python3 -m script.gen_requirements_all.
• For the updated dependencies - a link to the changelog, or at minimum a diff between library versions is added to the PR description.
• Untested files have been added to .coveragerc.

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[home-assistant]

Hey there @konikvranik, mind taking a look at this pull request as it has been labeled with an integration (rainbird) you are listed as a code owner for? Thanks!

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