Add MQTT subentry support for date, datetime and time platform

[jbouwh]

Proposed change

Add MQTT subentry support for date, datetime and time platform

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 subentry support for MQTT date, datetime and time entity platforms core#171396
• 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 updates the Home Assistant website documentation to reflect new MQTT subentry support for the Date, Date/Time, and Time MQTT platforms, so readers can configure these entities via the UI path (MQTT subentries) in addition to YAML.

Changes:

• Updates the MQTT platform pages (date, date/time, time) to mention configuring via MQTT subentries.
• Adds Date, Date/Time, and Time to the “Configuration of MQTT components via Subentries” list on the main MQTT integration page.
• Adjusts the MQTT integration platform lists (but currently introduces a formatting error in the discovery list).

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 5 comments.

File	Description
source/_integrations/time.mqtt.markdown	Adds subentry-based configuration option to the MQTT Time docs.
source/_integrations/date.mqtt.markdown	Adds subentry-based configuration option to the MQTT Date docs.
source/_integrations/datetime.mqtt.markdown	Adds subentry-based configuration option to the MQTT Date/Time docs.
source/_integrations/mqtt.markdown	Adds Date/Date-Time/Time to the subentries platform list, but includes a malformed Vacuum list item.

Comments suppressed due to low confidence (2)

source/_integrations/date.mqtt.markdown:18

• The YAML example that follows this code fence appears to nest date under a list item (mqtt: - date:), which is inconsistent with other MQTT platform docs and likely not valid configuration. Update the example to use mqtt: > date: with a list of entities.

```yaml

source/_integrations/datetime.mqtt.markdown:18

• The YAML example that follows this code fence appears to nest datetime under a list item (mqtt: - datetime:), which is inconsistent with other MQTT platform docs and likely not valid configuration. Update the example to use mqtt: > datetime: with a list of entities.

```yaml