Whoops, I was curious - turns out the estonian military did dig them, but they’re anti-migrant ditches, not anti-tank ditches. From the source article:

Border Guard Chief Veiko Kommusaar said that the PPA supports all activities that help ensure security in Estonia: "The PPA’s task at the border is to prevent cross-border crime and illegal border crossings. Our neighboring countries have been facing a migration offensive for years, and although people have not been targeted at the Estonian borders in this way so far, we cannot rule out that this will always be the case. Of course, the barrier ditches built by the Defence Forces would also slow down the movement of illegal border crossers, which is why they will also support the Border Guard in preventing illegal migration.

Yeah, your first impulse was right on the money with this one.