Imho Synology should add this line to there supportpage ( https://kb.synology.com/en-global/DSM/tutorial/Why_cant_I_connect_to_Package_Center):
Uninstall every incompatible package in the “Installed” window of the Package Center.
It can happen that installed packages are incompatible with an new DSM version. Apparently your Synology will display (imho) a very cryptic message “Connection Failed”. This even though one can access everything from and on the NAS and internet just fine.
Instead of trying to fix this issue and check or correct your network settings (as suggested in the Synology support article), just go to the package center and look for any incompatible package(s) and just uninstall them.
After this the issue is resolved and the connection of the package center is restored.
The author of this web-site cannot be held responsible for any eventual damages as a consequence of using the information found on this web-site. The author has done his best to (cross)check and verify information presented on this web-site but, there is no liability to guarantee against any eventual damages caused by the user. The user/reader is fully responsible for any eventual damages caused by implementing or misusing information found on this web-site.