[mitsubishi_cn105] use HEAT_COOL mode to enable temperature slider

[crnjan]

What does this implement/fix?

Changes AUTO mode as defined by Mitsubishi to match HA definition - HEAT_COOL.

Types of changes

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected) — policy
• Developer breaking change (an API change that could break external components) — policy
• Undocumented C++ API change (removal or change of undocumented public methods that lambda users may depend on) — policy
• Code quality improvements to existing code or addition of tests
• Other

Related issue or feature (if applicable):

• fixes AUTO Mode Change in ESPHome Breaks Millions of cn105 units built in control

Pull request in esphome-docs with documentation (if applicable):

• [mitsubishi_cn105] use HEAT_COOL mode to enable temperature slider esphome-docs#6469

Test Environment

• ESP32
• ESP32 IDF
• ESP8266
• RP2040/RP2350
• BK72xx
• RTL87xx
• LN882x
• nRF52840

Example entry for config.yaml:

# no changes

Checklist:

• The code change is tested and works locally.
• Tests have been added to verify that the new code works (under tests/ folder).

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated in esphome-docs.

[github-actions]

To use the changes from this PR as an external component, add the following to your ESPHome configuration YAML file:

external_components:
  - source: github://pr#15748
    components: [mitsubishi_cn105]
    refresh: 1h

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(Added by the PR bot)

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 76.42%. Comparing base (f59a101) to head (a0c32b1).

Additional details and impacted files

@@           Coverage Diff           @@
##              dev   #15748   +/-   ##
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  Coverage   76.42%   76.42%           
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  Files          58       58           
  Lines       12643    12643           
  Branches     1772     1772           
=======================================
  Hits         9662     9662           
  Misses       2556     2556           
  Partials      425      425           

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[github-actions]

Memory Impact Analysis

Components: mitsubishi_cn105
Platform: esp8266-ard

Metric	Target Branch	This PR	Change
RAM	29,488 bytes	29,488 bytes	➡️ +0 bytes (0.00%)
Flash	276,795 bytes	276,731 bytes	📉 ✅ -64 bytes (-0.02%)

📊 Component Memory Breakdown

Component	Target Flash	PR Flash	Change
[esphome]mitsubishi_cn105	4,363 bytes	4,302 bytes	📉 ✅ -61 bytes (-1.40%)

🔍 Symbol-Level Changes (click to expand)

Changed Symbols

Symbol	Target Size	PR Size	Change
esphome::mitsubishi_cn105::MitsubishiCN105Climate::traits()	205 bytes	144 bytes	📉 -61 bytes (-29.76%)

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Note: This analysis measures static RAM and Flash usage only (compile-time allocation).
Dynamic memory (heap) cannot be measured automatically.
⚠️ You must test this PR on a real device to measure free heap and ensure no runtime memory issues.

This analysis runs automatically when components change. Memory usage is measured from a representative test configuration.

[Copilot]

Pull request overview

Updates the Mitsubishi CN105 climate component to represent the unit’s built-in “AUTO” (auto-changeover) mode as Home Assistant’s HEAT_COOL mode so HA will allow setting a single target temperature via the UI.

Changes:

• Remap MitsubishiCN105::Mode::AUTO from CLIMATE_MODE_AUTO to CLIMATE_MODE_HEAT_COOL.
• Refactor traits() to derive supported HVAC/fan modes directly from the mode maps (avoids duplicating lists).

[bdraco]

Thanks @crnjan