Kind of solved:
The error logs pointed me to the file “Spine Universal RP Shaders > Shaders > Include > SpineCoreShaders > Spine-Skeleton-Tint-Common” (but could be different for someone else, read the error logs).
Opened the file. The top comment says “// Adapt this path accordingly if you have unpacked the Spine directory to another location.”, so I swapped them. In my case I commented “#Include “Packages”…” and uncommented to use “#Include “Assets/…”. Errors disappeared.
I could now right click and press “Reimport” on the “Packages > Spine Universal RP Shaders”. All files successfully reimported.
Problem: the stretchy man looks weird, I do use the “Example 2D URP Asset”. And sometimes the Console warns me that the stretchy man doesn't have "Solve Tangents" enabled in Skeleton Animation (under Advanced), but he do...