Support "climate" remote for Trinnity Series in Home Assistant

**Describe the problem you have/What new integration you would like**

I have a air coditioning unit from the manufacturer "Trinnity" (https://www.trinnity.de/)
I want to use the "climate" function and an ESP32 with this unit. Unfortunately
it is not supportet yet for the Trinnity-Series.

**Please describe your use case for this integration and alternatives you've tried:**

Acctually it is not possible to integrate the Trinnity-Series to Home-Assistant.
The Manual can be found here: https://www.manualslib.de/brand/trinnity/klimaanlagen.html
I could read out the IR codes for the TW33HP:

Remote codes Trinnity TW33HP

>>remote_transmitter.transmit_aeha

Degrees:
16
0x64,0x80,0x00,0x24,0x80,0xF0,0x00,0x00,0x00,0x00,0x00,0x92
17
0x64,0x80,0x00,0x24,0x80,0x70,0x00,0x00,0x00,0x00,0x00,0x12
18
0x64,0x80,0x00,0x24,0x80,0xB0,0x00,0x00,0x00,0x00,0x00,0xE2
19
0x64,0x80,0x00,0x24,0x80,0x30,0x00,0x00,0x00,0x00,0x00,0x62
20
0x64,0x80,0x00,0x24,0x80,0xD0,0x00,0x00,0x00,0x00,0x00,0xA2
21
0x64,0x80,0x00,0x24,0x80,0x50,0x00,0x00,0x00,0x00,0x00,0x22
22
0x64,0x80,0x00,0x24,0x80,0x90,0x00,0x00,0x00,0x00,0x00,0xC2
23
0x64,0x80,0x00,0x24,0x80,0x10,0x00,0x00,0x00,0x00,0x00,0x42
24
0x64,0x80,0x00,0x24,0x80,0xE0,0x00,0x00,0x00,0x00,0x00,0x82
25
0x64,0x80,0x00,0x24,0x80,0x60,0x00,0x00,0x00,0x00,0x00,0x02
26
0x64,0x80,0x00,0x24,0x80,0xA0,0x00,0x00,0x00,0x00,0x00,0xFC

OFF
0x64,0x80,0x00,0x04,0x80,0xF0,0x00,0x00,0x00,0x00,0x00,0xA2

Heat
0x64,0x80,0x00,0x24,0x80,0xA0,0x00,0x00,0x00,0x00,0x00,0xFC

Cooling
0x64,0x80,0x00,0x24,0xC0,0x10,0x00,0x00,0x00,0x00,0x01,0x23

Dehumidify
0x64,0x80,0x00,0x24,0x40,0x10,0x00,0x00,0x00,0x00,0x01,0xC3

Ventilate
0x64,0x80,0x00,0x24,0xE0,0x10,0xA0,0x00,0x00,0x00,0x01,0xB3

Health
0x64,0x80,0x00,0x24,0xE9,0x10,0xA0,0x00,0x00,0xE8,0x01,0x2E

IFeel
0x64,0x80,0x00,0x24,0xE8,0x10,0xA0,0x00,0x00,0x00,0x01,0xBB

Fan-Speed Low
0x64,0x80,0x00,0x24,0xE8,0x10,0x40,0x00,0x00,0x00,0x01,0x5B

Fan-Speed Medium
0x64,0x80,0x00,0x24,0xE8,0x10,0xC0,0x00,0x00,0x00,0x01,0xDB

Fan-Speed High
0x64,0x80,0x00,0x24,0xE8,0x10,0xA0,0x00,0x00,0x00,0x01,0xBB

Swing Horizontal
0x64,0x80,0x00,0x24,0xE8,0x10,0xA0,0x00,0x00,0x00,0x11,0xA7

Swing Vertical
0x64,0x80,0x00,0x24,0xE8,0x10,0xBC,0x00,0x00,0x00,0x11,0xB8

**Additional context**

Start by reviewing the ESP32 use case and the remote_transmitter.transmit_aeha examples for the Trinnity TW33HP, then compare them with the Trinnity manual linked in the request. Done means the Trinnity Series climate function is supported with the listed power, temperature, mode, fan-speed, and swing controls; no repository file or test is identified in the request.

Written by the indexing model from the issue text.