Why did a hot/neutral reverse lead to an HDMI cable shocking me?
Devices with grounded plugs need the ground connection for their mains input EMI filter Y capacitors to work as intended. Not providing ground means the grounded parts of the device, including HDMI connector, will float capacitively at half the mains AC voltage. This not only can hurt when touched but can also damage equpment if you connect two devices together and the capacitors get discharged by connecting the HDMI cable.
Devices with ungrounded plugs can also hurt, if their power supply has EMI filter Y capacitor between mains side and isolated side. Depending on the power supply implementation, the leakage current could be different depending on which way Live and Neutral are. In some countries you can connect the mains plug to wall in any orientation so usually the design does not care which way Live and Neutral are, but it can also assume which way Live and Neutral are connected, and leakage can be different if it is the wrong way.
I just tested with a two-prong 4K TV with a metal frame, and I can feel AC mains vibrations when sliding my hand on the metal. Multimeter says there is half of mains AC voltage from USB chassis to mains earth, and 130 microamps AC when shorting the USB chassis to ground. Reading does not change if I change the mains plug orientation to swap Live and Neutral.
Lesson is to do like most consumer equipment manuals say : disconnect devices from mains before making other connections between them.