LAN ports are auto sensing these days and thus don't need a crossover cable when connecting the Tx on one device to the Rx on another. WAN ports should also be auto sensing but it was just a long shot to try in case. It doesn't matter where it goes in the chain, it will just cross Tx & Rx anywhere between the ONT and Hub.
One other thought, are all 8 wires connected at each end of the structured cabling? 100baseT only needs 4 wires but GbE requires all 8.
CAT5e cables use 4 wire pair signalling scheme to achieve Gb connection. In CAT5 cables 2 of the pairs were dormant. Any modern install should use all 4 pairs.
Just had a possibly stupid thought. Are you sure you are connecting the ONT patch cable to the correct port on the patch panel that leads to the study.? Each port leads to a different room.