I think there may be a glitch or miss coding in the ATC training server. I have been doing it and have been unable to contact to the planes marked as a biplane. It shows them as unknown and doesn’t bring up a ATC contact screen.
The issue you are describing has been around for some time and is a known issue. Right now the best solution in the meantime is to work around those aircraft you are unable to contact and try your best. Thanks for the report and welcome to the community!