The joys of writing for help after hours of meddling with the issue and finding the answer 5 minutes later.
I noticed in the inspector that the AnimationPlayer had a strange value as a Root Node:
I don’t know how that …/… appeared there, but I changed it by setting the parent node as the Root Node.
This broke the animations, but to fix them I only have to fix the path of each track by removing the name of the parent node:
Now it works with no problem even with many scenes added.
Still, don’t know how that …/… value appeared there.
Sorry for the post.