Add routines documentation to Alexa Devices

[chemelli74]

Proposed change

Add routines documentation to Alexa Devices

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

• Link to parent pull request in the codebase: Add routine management to Alexa Devices core#166291
• Link to parent pull request in the Brands repository:
• This PR fixes or closes issue: fixes #

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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[Copilot]

Pull request overview

Adds documentation for newly introduced Alexa Devices routine-related actions, aligning this integration page with the upcoming Home Assistant Core feature work referenced in the parent PR.

Changes:

• Documented two new actions: alexa_devices.send_routine and alexa_devices.update_routines.
• Added an example showing how to run an Alexa routine via automation YAML.
• Updated the “Available actions” list to include the new actions.

[c0ffeeca7]

Please take a look at the comments by Copilot.

Out of scope for this PR, but we are changing how actions are documented:
https://developers.home-assistant.io/docs/documenting/integration-docs-examples#template-action

[home-assistant]

Please take a look at the requested changes, and use the Ready for review button when you are done, thanks 👍

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[c0ffeeca7]

A merge conflict appeared. Could you take a look?

[c0ffeeca7]

Thank you, @chemelli74 👍