To have legal protection insurance in case you get into a bigger dispute with the neighbor.
Legal protection insurance is not there to pay for dispute resolution between neighbors without any monetary value.
So for possible future verbal attacks (because there have already been some)
And against verbal attacks, there is not much help with terrible neighbors, not even legal protection.
1. Legal protection does not protect; it pays court and lawyer costs if the insurance recognizes a claim and the likelihood of winning a lawsuit is rated high. So please reflect on your words.
2. If you assess that a neighbor (or any other person) can cause problems, only information about the matter, diplomacy in communication, and reason as well as common sense help.
Being right does not mean getting justice.
But someone who tells me, "Come at me, stupid, then my legal protection will take care of it," would be suspicious to me as a person. I would not want such people living next to me. If something bothers my neighbor, I expect communication about the matter itself, not a letter from some lawyer. That’s just ridiculous.
This does not mean I reject legal protection insurance; I have one myself for things where there could be a costly dispute value, where I personally cannot influence, e.g., car-related issues.
Nevertheless, of course, I keep my fingers crossed that you will come to an agreement.
Best is simply to officially invite them for a beer/coffee/wine and discuss the fence or the problem together.
It seems you missed that after the move?! Whatever, it’s never too late.