Allow climate mode to be controlled via external entity (input_select / automation)

[snazzybean]

Description

Allow the per-room climate mode (auto, heat_only, cool_only) to be driven by an
external HA entity — e.g. an input_select — so that automations can change the mode
dynamically without going through the RoomMind UI.

Use case

A user wants their HA instance to check the weather forecast each morning and automatically
set the appropriate climate mode for each room for that day. For example:

• Forecast > 25 °C → set room to cool_only
• Forecast < 10 °C → set room to heat_only
• Otherwise → auto

Currently the climate mode can only be changed manually in the room detail view. Supporting
an optional climate_mode_entity (e.g. input_select.living_room_mode) per room would
make this fully automatable.

Suggested implementation

• Add an optional per-room config field climate_mode_entity
  (accepts input_select.* or input_text.* entities)
• When set, the coordinator reads the entity's state each cycle and maps it to the internal
  climate_mode value (auto / heat_only / cool_only)
• The manually configured mode in the UI acts as fallback when no entity is set
• The room detail UI shows a read-only indicator of the current effective mode when an
  external entity is active

Alternatives considered

Users currently work around this with manual mode changes or by configuring fixed modes,
both of which require intervention when seasons change.

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Originally suggested in #21.