AEG Chillflex AC integration

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

In addition to the already available ACs I'd like to request integration of the AEG Chillflex mobile AC series, in particular (in my case) the AEG Chillflex Pro Silence AXP26U558HW.

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

I have tried collecting the IR codes myself but am not sure if what I'm doing is the right way. Since the documentation of climate_ir states I should file a feature request to integrate a particular AC, I'm doing exactly this now.

**Additional context**

Start by reviewing the climate_ir documentation and the existing air-conditioner integrations it references. Determine what information is needed beyond the requested AEG Chillflex Pro Silence AXP26U558HW model and the author's collected IR codes; done means the requested mobile AC series is supported and its behavior is verified.

Written by the indexing model from the issue text.