Add Jellyfin documentation

[RunC0deRun]

Proposed change

Add the documentation for the newly proposed integration of the Jellyfin media system.

Type of change

• Spelling, grammar or other readability improvements (current branch).
• Adjusted missing or incorrect information in the current documentation (current branch).
• Added documentation for a new integration I'm adding to Home Assistant (next branch).
  • I've opened up a PR to add logo's and icons in Brands repository.
• Added documentation for a new feature I'm adding to Home Assistant (next branch).
• Removed stale or deprecated documentation.

Additional information

• Link to parent pull request in the codebase: Add Jellyfin integration core#44401
• Link to parent pull request in the Brands repository: Add Jellyfin logo and icon brands#2099

Checklist

• This PR uses the correct branch, based on one of the following:
  • I made a change to the existing documentation and used the current branch.
  • I made a change that is related to an upcoming version of Home Assistant and used the next branch.
• The documentation follows the Home Assistant documentation standards.

[frenck]

Some small changes requested. Could you take a look?

Thanks already! 👍

[frenck]

✅ Approved. Can be merged as soon as the parent PR gets merged.

[RunC0deRun]

Thanks @frenck for updating this PR! I saw the parent got merged, but did not get round to updating this one over the weekend.