vNext: Climate: skip devices without modes, offer only what the unit has

[Twintop]

Context

This is a bug fix and a small behavior change in preparation for Gree zone controller support. I found it while porting the changes I made for my own zone controller (Gree LE60-13/GH) to this project. The ducted unit behind a zone controller has no target temperature and no swing, and the climate entity offered both. The zone controller support itself will come in a later PR. Background and the full plan: https://github.com/Twintop/ha-gree-zone-controller/blob/main/upstream/README.md

Symptoms

1. If one device has an empty HVAC mode list (for example cleared in its options), the climate setup returns. No climate entity is created for that device, and none for any device after it in the entry.
2. A unit without a target temperature (no SetTem) still gets one in its climate entity when Heat, Cool or Auto is in the mode list. It shows 0, and a change only logs Property SetTem is unsupported on this device. Seen on the ducted unit of a LE60-13/GH zone controller.
3. A unit without swing still gets swing modes. The options form leaves the swing lists out when the unit has no swing, and the climate entity then falls back to DEFAULT_SWING_MODES and DEFAULT_SWING_HORIZONTAL_MODES. Seen on the same unit, which listed vertical and horizontal swing modes.

Change

1. continue instead of return in async_setup_entry() of the climate platform.
2. ClimateEntityFeature.TARGET_TEMPERATURE is only added when the unit supports SetTem.
3. SWING_MODE and SWING_HORIZONTAL_MODE are only added when the unit supports SwUpDn and SwingLfRig.
4. docs/entities.md says when the target temperature and the swing modes are shown.

Units that have these features behave as before. Units without them no longer show controls that do nothing. The state restore already checks for a missing swing list, so it needs no change.

Testing

• The test suite does not cover the entities. pytest: 254 passed, as before.
• Ruff passes. Mypy and Pylint show nothing new compared with 5.0-dev. I ran them without Home Assistant installed, so I compared the findings with the base branch.
• Real device, the ducted unit of a LE60-13/GH zone controller on Home Assistant 2026.10: before the change, its climate entity listed swing modes. With the change, it has no swing modes and no target temperature, and HVAC mode and fan mode work as before.
• Symptom 1 comes from reading the code. I did not set up a device with an empty mode list.

[p-monteiro]

I'll hijack this PR for commenting on all
They all look good. Thanks for the contribution

About the full plan:

• One thing that I think is of value is to extend the "zone_memory" behaviour to all devices that support target temperature, not only zones. Seems like it is a nice feature for all to have, to recall the target temperature by active mode. For ac_units/vrf_units they can read the mode from themselves, and for zones from the zone_controller as in the plan.
• It might be worth thinking about extending ZoneRole to be something like DeviceType to allow all the devices to have a type (ac_unit, vrf_unit, zone_controller, zone) and do logic based on that. Can be useful in the future.