Update nest instructions to use My Home Assistant and Nest Web Auth

[allenporter]

Proposed change

Update nest instructions to use My Home Assistant and Nest Web Auth which is needed:

• Existing Web Auth users need to update their redirect URLs to use my home assistant because of the breaking change. (The docs did not reference the callback url anymore, so this was not updated in Use My Home Assistant for OAuth2 redirect callbacks #22878)
• Existing App Auth users now have a path forward to fix OOB deprecation.

This temporarily removes the Youtube video walkthrough until an updated version is recorded.

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: Use My Home Assistant for OAuth2 redirect callbacks core#72449
• Link to parent pull request in the Brands repository:
• This PR is related to issue: Nest Error 400: invalid_request due to OAuth OOB/Desktop Auth deprecation core#67662

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]

Thanks, @allenporter 👍