Add support for IR Climate Remote for Toyotomi AC

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

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

**Additional context**

i can't find my ac in the list.
i have captured the code on oscilloscope and have code spreed sheet for most of the codes.
can anyone help me to choose the right platform or to create new for this ac.

this is the code spreed sheet i have recorded so far.
Libre Office:
[Toyotomi remote decode table.ods](https://github.com/esphome/feature-requests/files/8548557/Toyotomi.remote.decode.table.ods)

Converted to xls format:
[Toyotomi remote decode table.xls](https://github.com/esphome/feature-requests/files/8548558/Toyotomi.remote.decode.table.xls)

Here is the full code for power off (last state is COOL, TEMP 16, FAN AUTO, NO SWING, NO IONIZATOR)
Note: the captured code is taken from the ir receiver diode and it is inverted.

and here are in details:

Here is my recreated full raw data for the same code so you can extract the timings:
- remote_transmitter.transmit_raw:
# code: [9020, -4477, 659, -1670, 637, -548, 658, -546, 658, -547, 659, -550, 631, -596, 634, -550, 632, -574, 633, -571, 634, -571, 633, -575, 633, -575, 628, -575, 633, -572, 634, -573, 631, -576, 632, -570, 635, -597, 608, -597, 610, -595, 610, -595, 609, -1699, 609, -575, 631, -573, 634, -595, 610, -596, 609, -595, 610, -573, 633, -1697, 611, -594, 611, -1698, 609, -572, 634, -574, 631, -1698, 610, -576, 630, -20020, 612, -572, 659, -547, 652, -554, 659, -546, 662, -546, 656, -548, 660, -544, 660, -548, 658, -546, 658, -548, 660, -568, 636, -549, 658, -545, 661, -547, 658, -1671, 637, -1671, 636, -547, 659, -547, 660, -545, 661, -546, 659, -545, 662, -546, 660, -545, 661, -546, 660, -545, 662, -543, 661, -546, 661, -544, 662, -1668, 639, -1670, 637, -1670, 636, -546, 661, -40000, 8975, -4533, 611, -574, 646, -584, 636, -573, 610, -573, 635, -571, 660, -549, 659, -547, 661, -548, 658, -550, 658, -545, 664, -544, 661, -545, 663, -545, 661, -545, 662, -547, 662, -542, 664, -547, 661, -544, 662, -563, 644, -546, 663, -542, 663, -546, 663, -543, 664, -544, 662, -544, 666, -542, 662, -546, 661, -544, 663, -543, 663, -1646, 665, -544, 662, -1672, 638, -542, 666, -1670, 638, -545, 663, -19986, 664, -544, 663, -545, 661, -544, 665, -541, 665, -542, 663, -545, 664, -542, 664, -544, 663, -544, 663, -543, 664, -544, 661, -545, 664, -542, 663, -544, 663, -544, 664, -542, 665, -542, 664, -543, 666, -541, 665, -543, 664, -543, 665, -541, 666, -543, 663, -545, 663, -542, 667, -542, 663, -544, 664, -543, 665, -542, 662, -1670, 641, -542, 665, -1670, 639]

Review the attached Toyotomi decode spreadsheets, images, and the raw transmission example first. Determine how the captured timings and remote states could become an ESPHome integration; done would mean documented support for this AC remote, but the issue names no source files or tests.

Written by the indexing model from the issue text.