After spending so many years in HVAC and construction, etc. I have never been a fan of home warranty companies. I did always say at least buy one for the first year only as it will cover all but especially the A/C system.
You can have an inspection on A/C system by a qualified A/C company, but this does not guarantee no leaks or problems will not occur. I have been on many A/C calls and the homeowner just bought a house within last year and the system was low on freon. A/C companies will do an inspection but leak checks are more to perform and no guarantee on leaks. No A/C company will guarantee against leaks even during an inspection. Now the new homeowner is stuck with a problem and no way to prove it but the leak was probably there before the house was sold. Now the home warranty company is stuck with changing out the system. They may be slow but at least it’s out there pocket and not yours. I know what has transpired here when finding this but no way to prove it. A leak can start at any time but usually by how much the system is low tells you how long a leak has been there from experience, but again, no way to prove it so as A/C professionals even during an inspection we have to keep to ourselves.
So for one year at least protect yourself with a home warranty covering your major mechanical fixtures. As there is no way to know when they will break down and leaks are very hard to find sometimes to actually not being able to pinpoint.