Hi I'm not an expert but it could be a worn/stuck relay.
Just had regas yday , no joy , warm
air , actually got a refund cos it didn't work , who knew 🤷
Guy said could be pump or sensor , so as you do I headed to Google and YouTube.
By chance I stumbled across a post about tapping the relay with a screwdriver driver.
Sure enough I tried it and the clutch kicked in and I briefly had cold air.
However as I've now learned the ac cycles on and off , and after first cycle it wouldn't re-engage , UNTIL , another tap. My takeaway is that it's the relay so I've ordered a new one and hopefully that cures it , fingers crossed.
Will report back later.
Location of the small relay box in my car ( 2010 EX ) is next to window washer top up , very accessible.
To remove the relay I had to grab , very gently , with some grips.
The box lid itself just has two squeeze? clips , very easy .
All I will say is be VERY careful if tapping relay with engine running, I nearly dropped screwdriver and it's right where all the belts are spinning rather fast :-)