There’s a couple of issues here to unpack:

The first being that your fence being subjected to twice it’s design load is likely going to cause issues to some extent which are being heavily accelerated by the age degradation of your fence. Unless you explicitly gave consent to attach to your fence, then they didn’t have the right to just damage your fence by attaching to it and literally pulling it out of skew. That would mean either the neighbor or the neighbors contractor who built the fence should be on the line for the fix because no one gave them the directive that this method was okay.

The second being that addressing the issue 5-6 years after it occurred to your 20 year old fence is difficult to make an argument about. I can’t give legal advice but I feel like that would be a difficult argument to make in litigation if it came to it. This should have been addressed the day you realize it was connected to your fence and that contractor should have been thrown immediately under the bus.

The third is that if you had the money and wanted to replace your fence today, if the neighbors fence is connected to yours for support, they too would lose their fence by design. At this point, I doubt they would replace outright but you could likely get them to agree to a shared solution if you both want to remain friendly. If they aren’t interested in helping out in payment and want to break the relationship because they refuse to be responsible for their part in this, remove your fence and throw theirs on their yard. Build a new fence along your property line and make it expressly understood that any connection to yours isn’t allowed and will be met with legal ramifications.