This is the ground rod that they used when installing the AC.

I did not realize it was so pathetic till one of the dogs dug it up

Have now replaces with a heavier gauge wire and proper 1mt rod.

Just out of curiosity does the AC unit in the house also have to be grounded?

I'm guessing as the inside and outside unit are connected by the copper pipes only the outside unit needs to be grounded.

Follow the manufacturer's instructions regarding earthing as there's usually only one earthing terminal provided for an external connection.

Earthing of other components and sub-assemblies are done by the manufacturer using internal wiring etc.

Yeah, it's almost funny what Thai's do for ground - I surmise they just don't get it. For me, I had a 2nd A/C unit installed on the same circuit as A/C-1 (I have it on 32A breaker) and the 2nd unit was only 2m away from supply with ground. They ran 2-core to the supply and drilled a hole in the concrete for the ground (which easily came out). Unbelievable.

OP - I would give that stake a pounding well into the ground and you're probably good. If your house has a ground system, probably better to re-connect to that if easily available.

The local electricians where i live claim, " We don't need ground rods anymore. We have RCDs now. It is safe".

I am skeptical about their claim. Can anyone verify? Do we really not need ground rods if there is an RCD / ELCB installed somewhere?

Class-1 devices need ground - whether RCD protection or not.

As I understand it, if you already have a grounding system, the ground wire going to the indoor unit should be extended and used for the outdoor unit ground too. if you don't yet have a grounding system, that's when you install something like the PIC in you OP (only do it better)