Add documentation for Litter-Robot integration

[natekspencer]

Proposed change

Add documentation for new Litter-Robot core integration

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 litterrobot integration core#45886
• Link to parent pull request in the Brands repository: Move litterrobot images to core_integrations brands#2228
• This PR fixes or closes issue:

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.

[probot-home-assistant]

It seems that this PR is targeted against an incorrect branch. Documentation updates which apply to our current stable release should target the current branch. Please change the target branch of this PR to current and rebase if needed. If this is documentation for a new feature, please add a link to that PR in your description.
_{^{(message by DocsTargetBranch)}}

[natekspencer]

@frenck hopefully those are all the updates needed now!

[frenck]

Thanks, @natekspencer 👍