Most AC indoor units have some sort of flap or swing at the air exhaust which opens/closes when you power it on/off and which also directs where the cold air is blown (often with a ‘swing’ setting or something like that). If your AC has such a flap, you could use a door/window sensor to dectect whether it’s currently powered on or not.
Here’s a picture of what I mean:
Don’t think it didn’t cross my mind… 
That’s not a bad idea but I have a central AC not standalone.
Does it have a power LED?
If so, you have a couple of options:
Use a light dependant resistor to test if the LED is on or off. Or if you are feeling a bit more adventurous, open it up and and connect an optocoupler in series with the LED.
Getting that signal back to HA can be done a number of ways. Probably the simplest and cheapest would be with an ESP module of some description.
Ah, okay - then it’s a little more difficult. 
Those central AC units are not so commonly seen here in my country. I don’t think that fetching the IR signal with a reciever would work well in this case if you only have one button to toggle the power state, because it will go out of sync if the signal isn’t detected correctly every time. Using a temperature sensor on the air outlets isn’t the best option either, because you can only detect if the AC is blowing out cold air right now or not. Maybe a combination of these two solutions would deliver a reasonable result.
Nevertheless, I guess it’s pretty hard get the accurate power state into Home Assistant with these units. 
If you are able to make modifications, an inline power monitor to the AC like the sonoff pow would give you the state
What about a wind speed sensor?
Not sure if this would work, but maybe you could put a temperature sensor in front of the vent and do a mathematical comparison between the detected temperature and the outside temperature?
An in-wire Sonoff, good one. Or if you can access the power plug: just use a smart power plug. E.g. Neo Coolcam Smart Power Plug does power measurement. Using it to detect if my set top box is on or off.
I’ve wired little temperature sensors to ESPs running espeasy to measure my pool temp.
Air temp would be easier, but I’m not sure how you would put a sensor in front of the vent without it looking bad.
Here’s some info on wiring the sensor
temp sensor
audio sensor/microphone to listen for the air flow might work, but I expect the detection algorithm may be tricky.
Someone already suggested power sensor on the ac power lines. Could also maybe put a vibration sensor on the ac unit if you have access to it, depending on how much it moves during operation.
Thanks for all the ideas! Some might be tricky as the AC can go into “snooze” once it hits appropriate temparture which would stop wind / noise / power consumption but it’s still on (and will kick in eventually again) but that’s still better than nothing
How do you tell now whether it is on or off? If something is observable it is recordable.
Out of the box suggestion.
See if you can find on/off codes for your AC. There are ir databases online, and your ac might support discrete on/off codes even if your remote doesn’t.
Then make an ir blaster to control your AC
I recently made one
ir blaster
There is a control button with an indicator light… But I couldn’t think of a good elegant solution for observing this…
That would be ideal but I couldn’t find any indication an off code exists nor did I find any online (doesn’t mean it doesn’t exist but I didn’t find any :))
I happened to be reading this earlier
ldr
Someone said he used it to detect washing machine status.
So you might be able to read the indicator light, on off should be pretty easy with a little tweaking.
Is the control button a wall-mounted unit? Something like this ? If yes, then you might want to peek behind the unit. You should be able to find power cables. You can then tap into the power cable and use an inline Sonoff POW(2nd Gen). Stating the obvious, but don’t forget to switch the mains off when doing this.
Lastly, I hope it is not a rented property. (which makes any modifications tricky due to legal/contractual requirements)
Maybe an HEM in the circuit breaker box to determine power usage. Can watch it for a while to determine your low limit (on/off) then create automation to turn virtual switch on or off based on the power. I have something similar for my washing machine.
- alias: Washer Turn On
trigger:
- platform: numeric_state
entity_id: sensor.washing_machine_power
above: 10
for:
seconds: 60
action:
- service: input_boolean.turn_on
entity_id: input_boolean.washer_status
- alias: Washer Turn Off
trigger:
- platform: numeric_state
entity_id: sensor.washing_machine_power
below: 30
for:
minutes: 3
action:
- service: input_boolean.turn_off
entity_id: input_boolean.washer_status
It all depends on how “invasive” and “handy” you are. Assuming there is a control pannel on the wall with a LED indicating the status of the device, I see two possible options:
Thanks for all the ideas.
I will try to look behind the panel but I doubt there will be room in there to place a sonoff though.
Will see if maybe I can make it work with watching the led otherwise.