Save client identifier from Plex auth for future use

[jjlawren]

Description:

The client identifier generated during the Plex OAuth-like authentication may be needed in the future to utilize the returned token. The client ID was originally discarded, but this saves it to the config entry in case we need it eventually. No current functionality will break if this requirement is added by Plex, but future component features may need it to be available.

Checklist:

• The code change is tested and works locally.
• Local tests pass with tox. Your PR cannot be merged unless tests pass
• There is no commented out code in this PR.
• I have followed the development checklist

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• The manifest file has all fields filled out correctly. Update and include derived files by running python3 -m script.hassfest.
• New or updated dependencies have been added to requirements_all.txt by running python3 -m script.gen_requirements_all.