Update nest documentation with common misunderstandings

[allenporter]

Proposed change

Many users are confused and hitting problems either because they are missing migration steps, missing setup steps, not reading the whole page for troubleshooting steps, or misinterpreting what is said and making incorrect assumptions. These are all understandable since there are so many steps, but this attempts to add some additional clarifications, screenshots, and in-context detail to help users make sense of this.

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:
• Link to parent pull request in the Brands repository:
• This PR fixes or closes issue: fixes #
  Nest integration not working on Raspberry Pi4 core#74774
  Updated Instructions not working core#74552
  this guide is not working, Unable to link NEST Google since 2022.7 #23330
  Issues with "Link Google Account" section #23299

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 👍