IF this is true, it's a perfect, real-world, textbook example of rent-seeking. The classic example is putting a chain across a river used for commerce; this is exactly the same, updated for modern technology. Excellent! Economics students take note!
You're wrong on this one. The Internet was designed by DARPA precisely for this kind of situation, namely routing around damage to the network because of war damage.
The end effect of attempting to cut cables and prevent repair ships from... ahem... repairing the cables in Hormuz during a war or otherwise is that traffic will be transparently diverted to other cables in the network.
Nobody will notice, except for the neighbouring Gulf states, who will probably see traffic slowdowns, as their other connections must take the packets, and _possibly_ (but that's a long shot) more expensive Internet pricing.
Literally nobody in the rest of the world will notice any sustained slowdowns on packets. This is completely unlike the oil price hikes, which will remain for at least as long as the US and Israel keep inflaming the region.