Add cache to split_entity_id

[bdraco]

Proposed change

Add cache to split_entity_id

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)
• 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 #
• 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.

The integration reached or maintains the following Integration Quality Scale:

• No score or internal
• 🥈 Silver
• 🥇 Gold
• 🏆 Platinum

To help with the load of incoming pull requests:

• I have reviewed two other open pull requests in this repository.

[emontnemery]

Powers of two are best number 😄

[balloob]

Did we time this if this is faster? Splitting a string isn't that expensive?

[bdraco]

Yes, its about 30% faster on average even with the lru overhead. The only time its slower is when we evict from the lru cache which will likely never happen with the size of the cache.

We can also dump the caching in logbook as well in #71359

[balloob]

That's pretty wild, it's such a small function.