Small sabotage attempts at water towers, power plants etc. Nothing actually happens but it gets in the news and people think something COULD have happened.
It keeps people stressed a bit all the time and they start wanting things to go back to "normal" at any cost - even by letting Russia keep the bits of Ukraine they assaulted.
Most likely, they prop it as a huge win domestically, so that the public keeps thinking they are winning and become easier to placate.
Then why don't these sabotages happen in US waters if it's so easy to get away with it?
Neither the EU countries, nor the US have enough ships to patrol or escort every civilian ship that happens to parse over an undersea cable.
Assume that the Russian shadow fleet starts targetting US cables. What would, could, the US do? The US government could easily retaliate by simply opening the US weapons depos to the Ukrainians. Target US infrastructure and Ukraine gets whatever it wants. The EU can't really do something similar.
Technically you're not wrong, if the EU navies where large enough, they could just escort every single civilian ship, but that's not realistic.
E.g. perhaps something along the lines of prison for captains who were 'derelict in duty', rewards to crews who grass and seizing ships that, by dragging anchors 'by accident', have proven themselves unseaworthy etc.
Good luck enforcing that. The "shadow fleet" ships all operate under flags of convenience and ownership is hidden behind layers upon layers of shell companies.
In contrast, the North and Baltic sea are a hodgepodge of individual nations' 12-mile zones, the Baltic Sea operates under an entirely different set of agreements that guarantee free passage, and it's not really deep so submarine infrastructure like cables can be hit by anything from anchors to divers with explosives.
We cannot prevent it, we can only detect it and (try to) identify who did it. The planet (some special interest areas) are constantly being monitored (satellites, surveillance drones) and when large ships are not being 'naughty' (switch of transponders) it's relatively easy to put two and two together.
As a side-note, Russia's playbook it to cause small and frequent sabotage(s). Small enough to not cause massive retaliation (i.e. it forces someone to destroy their railroad infra by causing thousands of derailments within one hour), and frequent enough to cause actual damage.