https://asp.mvc-tutorial.com/routing/routing-templates/
The solution turned out to be to use a '*' character in front of the token, like this:
[Route("api/GetString/{*objectPath}")]
I don't get the leading slash, but that's fine, I can prepend that before the search. Of course, after 3 hours of searching, I find this 17 minutes after posting the question :-)
Best regards and HTH someone