Hello Oliver
It seems that SSH Public Key Authentication is only available for local username authentication. This can be seen in the following Cisco documentation:
As I don’t have personal experience with SSH Public Key Authentication in combination with an AAA system, doing a bit of research online, there seems to be the consensus in general on other sites focusing on RADIUS and TACACs that this is not possible. Although it is not stated clearly anywhere official, the general experience of users seems to indicate that it is not possible.
I hope this has been helpful!
Laz