Preserve the working comparison
Apple recommends connecting a problematic external display directly to the Mac when it is normally attached through a dock or hub. If the direct route works, record that result before changing software or replacing the television.
The result narrows the investigation to the changed route, but it does not alone prove the dock is defective. Its power, port configuration, cable or supported multi-display combination may differ from the direct connection.
Reintroduce one dependency
Use the same TV input and programme while reconnecting the dock. Add other displays only after checking the television. Compare the available resolution and refresh rate in macOS. A route that still shows an image at a lower mode has a different limitation from a route that is entirely undetected.
Check the exact dock model’s primary documentation for the Mac, port and display combination. A connector being physically compatible does not establish bandwidth or support for all attached screens at once.
Describe the boundary precisely
A useful support report states the Mac model, direct route that works, dock route that fails and whether extra displays change the outcome. It lets the manufacturer assess a supported combination rather than a generic “Mac HDMI problem.”
Keep the direct connection available as a temporary usable configuration where practical. Do not change a working service account or reinstall a player simply because an intermediary changes the computer’s display output.
Questions answered
Does a direct connection working prove the dock is broken?
No. It identifies the changed route for further specification, power and configuration checks.
Should I change the programme during the comparison?
Keep it fixed so the physical route remains the main variable.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.