macbook pro diagnostic online session

It is not clear exactly what model of Mac you have and whether you are attempting a Self Service Repair. Apple's Self Service Repair is only available for a limited number of devices (probably only the most recent since this announcement was made by Apple).

The Apple Self Service Diagnostics page mentions that devices must be running iOS 17+ or macOS 14.1+ to be able to initiate an Apple Self Service Diagnostics sessions (Beta versions are not allowed):

https://getsupport.apple.com/self-service-diagnostics

Here is an Apple article regarding the new Self Repair Program:

https://support.apple.com/self-service-repair

Don't expect too much from these other diagnostics since they have become much simpler & less reliable over the years. Most times even the Apple service diagnostics will not reveal any hardware issues.

I think the "offline diagnostics" are actually the same as the basic consumer online diagnostics. Apple isn't very good a descriptions and dialog information. I'm not certain why you are seeing the message about no sessions found, but it is probably due to Apple allowing some devices to run the Self Repair Diagnostics. I don't think I've worked on any Mac which is compatible with the Self Repair Program yet. Apple doesn't always do a good job with their interfaces & messages, or documentation.

If you are able to run the Apple Diagnostics without needing to start any sessions, then you are running the standard consumer Apple Diagnostics that have been available for years and that is all you would have available if the Self Repair Program is not an option for you. I believe they have always mentioned "offline", but I don't pay attention to the messages since I just press Return if needed to run them.

Use Apple Diagnostics to test your Mac - Apple Support