Electricians

Having gathered more info from your other replies, well, let's say the same but quicker... you know the meme :

'xcept here it'll be GROUND ALL THE THINGS!

The slab, the pipe, the Cat6 conduit, ground it all. If I was in my line of work, there'll be a 6mm² ground wire between both houses.

(Image credit Allie Brosh' excellent "Hyperbole and a half")

Normally, the bonding arrangement should also include a connection to the slab, by way of a piece of rebar poking up from the foundation. The point of bonding is to attach as many normally-grounded things together, and this usually happens around the service entrance, as a matter of convenience. Here in California, we might use an outlet box on the side of the house to reveal the rebar bonding link, but perhaps Canada puts it somewhere else due to the heat loss in winter.

I should add that I might have a bit of a complex grounding situation. I'm sharing a well and internet connection with my old house which is about 200' away on the same property.

That the new house is a subordinate structure has a small impact on how the bonding is set up. Since neutral and ground are already bonded at the service for the old house -- and I'm assuming there are no transformers used over that 200 ft wire run -- the new house must make sure to not bond ground and neutral. Indeed, after the bonding point in the old house, ground and neutral should never be intentionally bonded anywhere else. A mistaken bond can lead to the "objectionable currents" I mentioned earlier, but this is diagnosed the same way by turning stuff off to see if the voltage goes away.

But apart from this difference compared to the old house, all other things should be bonded to the new house's ground: water fitting, shield wires (if present) on any telecom wires, gas pipe. Because of your substantial distance between the two structures, it's possible that the grounding system would have been simpler if the electrical service was "derived" using a transformer, such that the new house would have a different service that would be bonded to its ground, just like a standard home. But that ship has sailed.

A brass fitting on the poly pipe bringing water into my new house is at the same potential as my slab - that is, 20V from electrical ground.

Once the source of your ground current is found and mitigated, you may also consider bonding this water fitting to ground, at both the old and new homes. That way, if a future issue arises with the ground, it won't be using the water as a conductor and causing a shock risk. Even if you don't find the source of ground current, this is still a good idea, since some ground currents are perfectly natural -- especially over 200 ft -- but the risks posed by them can be mitigated by forcing everything to be at the same voltage (thus no more shock risk).

Indeed, one way that electricians test for the magnitude of a ground fault is to set up a temporary bond and measure the current through it. If large residual currents start to flow, it might indicate that the proper bonding elsewhere is faulty. I think you correctly assessed your issue as definitely non-trivial and an electrician should investigate thoroughly.

I'm using Cat6 copper to share the internet and am only getting 100Mbps on the link.

Seeing as you've already buried the cable, my comments are a bit late. But ground issues for twisted-pair Ethernet cables between buildings is a known issue, with no real solutions other than using non-conductive fibre optic cables or wireless links to bridge between buildings. At my work, we somewhat regularly see issues with twisted-pair cables running between buildings on campus, with the typical result being the death of the switch port where the cable plugs into.

It's true that Ethernet is supposed to use mini-transformers to isolate the grounds at either end of the cable, but that's not the only issue: having 200 ft of conductor means that a distant lightning strike induces a sizable voltage on these wires, even when underground. Those mini-transformers behind each port might only tolerate 2000 volt spikes, so if they've already been damaged by induced voltages, degraded performance would permanently affect the switch port, although the cable might still be intact.

You may want to re-verify your Ethernet cable using different equipment at the ends, but it may only be a matter of time until future issues arise. At work, we solved most of our woes by changing to wireless APs (eg Ubiquiti) aimed using line-of-sight for existing buildings. Between new buildings, we run fibre cables and then use a converter to turn it back into standard twisted-pair Ethernet once inside the structure.