Add Playstation Network Documentation

[JackJPowell]

Proposed change

This change contains the documentation to accompany the new PlayStation Network integration found on PR#133850. It has followed the quality scale recommendations and attempts to cover all bronze level tasks.

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 logos 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

• New PlayStation Network Integration PR#133901
• The associated brand images were included for the custom integration and are still up to date. Brands PR

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.

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