Hi Andreas,
before we go into the details, try this:
Go to Preferences [CMD-e] and there to Files. Define the Texture Path where all your textures for this model are. You can have up to ten with this option.
If that doesn’t reconnect all textures, try in the Texture manager the “Localize Filenames”.
Is it working? If yes, save the scene file “Save Project With Assets…”. This creates a new Folder with all Textures inside.
Textures should normally live in the “tex” folder inside of a project folder, as created with the “Save Project With Assets…”.
If all of that isn’t helping, I can offer to set up an upload link and you share the object in the file and leave just the Material you have used for it in the file, nothing else. Just these two things will help me to see what is going on.
All the best