I have seen pictures of canals running across a continent, how is that possible with only two canals per city?
Here is an example posted to reddit:
https://i.redd.it/7rrz1d51oii21.png
You can have three canals per city. They just can't be adjacent to both another canal and your city. In the screen you posted, there's a city between three lakes that had three canals -- each one connecting to a lake tile.
Also in the SS you posted, there are actually four canal systems, with the before mentioned city being used as a junction for the two long canals. The longest one starts at the top and goes to the bottom-left. It's basically: Ocean, canal, city, canal, lake, lake, canal, junction city, canal, lake, lake, lake, canal, panama, panama, panama, lake, city, canal, ocean.
The second longest goes from the top the the bottom-right: Ocean, canal, city, canal, lake, lake, canal, junction city, canal, lake, lake, canal, city, canal, lake, lake, canal, ocean.
The third goes from the top to the left. It's: ocean, canal, city, canal, lake, lake, lake, lake, canal, ocean
The last system is very small and it's in the bottom-right corner. It's: city, canal, ocean (which is pointless because he/she already has a harbor in the ocean, but I suppose you could argue that the ocean connects the two systems but then again that would make an infinite loop in most cases).
This player make very good use of placing a city one tile away from two different lakes or between a lake and an ocean. This enables them to do several: lake/ocean, canal, city, canal, lake/ocean connections. They even do with using the panama canal (lake, canal, city, panama x3, lake); however, this is obviously canal overkill in most instances.
Anyways, pre-planning for canals is very important when settling cities as soon as you pop your first settler. Canals are obviously very situational, but they can pay off tremendously if planned correctly. I'd definitely recommend making full use of the canal map tacks so that you don't accidentally place a district where you will later want a canal.