Add new Home Connect washer related programs

[Diegorro98]

Proposed change

Add the following programs:

• laundry_care_washer_program_hygiene_plus
• laundry_care_washer_program_rinse
• laundry_care_washer_program_spin_drain

Also shortened washer related programs

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 new Home Connect washing machine programs core#157174
• 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

This PR adds three new Home Connect washer programs (hygiene_plus, rinse, and spin_drain) to the integration documentation and alphabetically reorganizes all washer-related programs for improved readability and maintainability.

• Adds three new washer programs: Hygiene, Rinse, and Spin/drain
• Alphabetically sorts the washer program list (lines 408-440)
• Maintains existing formatting and structure consistent with the rest of the documentation

[Copilot]

The alphabetical ordering is incorrect. "Super 15 min" (line 437) and "Super 15/30 min" (line 438) should come after "Towels" (line 436), not before "Water proof" (line 439). The correct alphabetical order should be:

• ...Towels
• Super 15 min
• Super 15/30 min
• Water proof
• Wool

[Copilot]

The display name "Hygiene" doesn't match the program identifier which includes "plus" (laundry_care_washer_program_hygiene_plus). For consistency with other programs where the display name matches the identifier (like "Cotton eco"), consider updating the display name to "Hygiene plus" or verifying that "Hygiene" is the correct user-facing name.

Suggested change

	- **Hygiene**: `laundry_care_washer_program_hygiene_plus`
	- **Hygiene plus**: `laundry_care_washer_program_hygiene_plus`

[c0ffeeca7]

Thank you, @Diegorro98 👍