The rule is - if it's going inside the wall, only a licenced electrician can do it. Yes it also extends to things like speaker or HDMI cables. It's mad.

Mad, indeed. It's hard to imagine those rules are followed, especially for speaker wires and HDMI cables.

HDMI cables? Sounds like protectionism. Invent rules to make yourself more work.

Aren't there power delivery versions of HDMI?

I can understand requiring a license for any power wires behind walls.

I could also see the possibility that it's just an old law that doesn't consider data-only cables which don't have the safety issues that wires carrying power do.

It's definitely an old law that never took data cables into account, but the current interpretation is that any cable that carries electrical current has to be installed and certified by an electrician.

While HDMI can provide a tiny bit of power and there are active cables for signal boosting, HDMI was never meant for power delivery. You might be mixing it with HDMI with Ethetnet.