Quick post, yes they work, and one fell apart so I took a picture.
Fiber Optic HDMI cables are readily available on sites like AliExpress and eBay these days and have been for a few years now.
I recently bought a few extras and one turned out to be poorly assembled and it fell apart, giving us a look at the inside:
This is the transmit (source) side, there's some circuitry on the bottom, and we can see some kind of blob presumably containing a VCSEL or laser transmitter. It looks like a QFN packaged IC may have been removed from the design, or it's possibly wire-bonded in there and not visible in the picture.
HDMI to fiber conversion either requires multiple fibers (one per data line, there are 4 including clock), or a serialiser/deserialiser chip to put all 4 into one signal, it looks like a single fiber is used but not entirely sure.
We can also see decent strain relief with a metal clamp holding in a moulded cable retainer.
These cables do have some electrical signalling making them not entirely galvanically isolated, this is a simplification of the problem by presumably passing the DDC (I2C like) negotiation bus on the electrical wires and running the video signal over fiber. These signals are pretty low speed so are likely able to work over quite long distances provided sufficient wire gauges and perhaps a signal buffer are used.
Compatibility seems good, though I have found one of my on-camera HDMI monitors won't properly power up the transmitter. Presumably these cables use all of the 5 V power available to an HDMI cable, while the battery powered monitor may limit the power supply more than a typical PC.
DisplayPort cables also seem to work, though I suspect they may have issues with the more esoteric parts of the specification like two-way communication. Also, they are slightly wider than a normal cable, so adjacent connectors may interfere (though I have been able to force them to work).
I super-glued the chassis together and the cable kept on working.