They don't need to sail through territorial waters. The Baltic is a shallow sea (~55m deep on average, 460m at the deepest point) and an anchor chain can be 200-300m long. So dragging an anchor on the bottom of shallow international waters provides just the right combination of plausible deniability and an environment with low legal repercussions.

This is one of the reasons it doesn't happen in the Atlantic. By the time you are out of territorial waters, in general the required anchor chain length puts the incident outside of any plausible deniability.

If they want to sail in or out of the Baltic it's through Denmark.

A ship that leaves port to cut a cable and then back to the same port loses all plausible deniability.

But what kind of inspection and registration prevent a ship from minding its own business in any Baltic port, say Sankt Petersburg, and then just drag an anchor across some of the cables on its way out or to any other Baltic port?

The whole thing with this kind of sabotage is that looks like a ship doing ship things except with a "defective" anchor system, "oops".

I would expect them to be capable of multitasking.