I'm having this same problem since I updated JDownloader2 as well.
Did some testing and found out some specifics...
The clipboard button is working, and it is sending the data to the docker correctly (this can be verified by opening the Clipboard, paste something, hit Submit, then click the "Add New Links" button. Your pasted link will show up there. )
The issue seems to be the "Clipboard Observer" is not starting when you start the docker, even if it is checked. So if you uncheck and then recheck the "Clipboard Observer" icon, it then starts working. Note that again if you shut down the docker and restart it, you will have to do this each time, because it isn't saving the setting.