A VIA flight A->B->C will not be shown on an "airport schedule" at city A as an A-C flight via B.
In other words:
Going to a particular airport "A", and clicking on a schedule of an airline X operating a via flight A-B-C
E.g. at airport A
From A - to B --- will be shown
From A - to C --- will not be shown at all
From B - to A --- will be shown
From C - to A --- will be shown, via B
Then, at airport C
From C - to B --- will be shown
From C - to A --- will not be shown at all
From B - to C --- will be shown
From A - to C --- will be shown, via B
A VIA flight A->B->C will not be shown on an "airport schedule" at city A as an A-C flight via B.
In other words:
Going to a particular airport “A”, and clicking on a schedule of an airline X operating a via flight A-B-C
E.g. at airport A
From A - to B — will be shown
From A - to C — will not be shown at all
From B - to A — will be shown
From C - to A — will be shown, via B
A-C (via ‘B’) doesn’t have an entry under the airport pair, but both segments of the flight are displayed under the A-B pair for scheduling purposes. See image below:

For the airport pair listing, it only shows the segments that depart from that specific airport. In the screenshot, my HND-CTS-YVR flight appears under HND-CTS, because the CTS-YVR portion doesn’t depart from HND but rather CTS. That it’s a continuation of EAV 55 from HND doesn’t matter.
Changing pricing or onboard service for the segment is done through the Inventory page for each airport pair. However, as I’ve already set prices and service for HND-CTS due to the 35 other daily flights that I offer, I only need to configure CTS-YVR and the reverse.
Edit: emoji suck. People who use emoji also suck. Forum software that substitutes emoji sucks most of all.
But I think this is still a bug... then why would C-A be displayed but not A-C, under the airline's schedule for Airport A .
In old UI the flights in schedules were displayed properly.
Also, imagine you fly via non-transfer airport. A-NT-B should show in schedule at airport A, because passengers are either A-NT, or A-B.
This is regardless of how the flights are displayed in Inventory, airport schedule display has nothing to do with Inventory display.
Ah. You weren’t saying what I thought you were saying. I saw ‘airport schedule’ and thought ‘scheduling at X airport’ instead of ‘flight schedule’ or ‘timetable of airline at airport’.

I see it too, continuing with the example flight that I used before with different screenshots, my timetable/flight schedule at YVR doesn’t show the inbound (EAV 55) operating HND-CTS-YVR. Nor is there any indication that EAV 66 continues past YVR-CTS.
But didn't that happen in the old UI? My African subsidary has a lot of Via flights and the airport schedule page often dropped information, particularly if you changed it to 'local time', for some reason.