How to identify the operating carrier of a codeshare flight without a ticket?

I am trying to figure out how to determine which airline actually operates a codeshare flight, relying only on airport websites (as I don't have a boarding pass since I'm not the passenger). While some airport websites (like SFO) clearly show exactly who the operating carrier is, many others don't. I am looking for the general patterns or tips to identify them across various airport sites.

For example, here is a flight from Seoul-Incheon (ICN) to Qingdao (TAO) that appears to be a 3-way codeshare:

Airline/Flight No.:
MU2040 / CHINA EASTERN AIRLINES
FM3078 / SHANGHAI AIRLINES
KE5853 / KOREAN AIRLINES
Terminal: T1
Check-in Counter: H01-H18
Gate: 130

How can I tell which of these three airlines is the actual operating carrier using only the information available on the airport website? Any general patterns or alternative resources (besides the airport website) would be greatly appreciated!

Some flight tracking websites give that info, e.g. https://www.flightaware.com/live/flight/CES2040 (same as MU2040), https://www.flightaware.com/live/flight/KAL5853 (same as KE5853) and https://www.flightaware.com/live/flight/CSH3078 (same as FM3078) all indicate that China Eastern is the operating airline:

Airport websites are unreliable: may or may not have the info. So it is best not to rely on them. E.g. from https://www.airport.kr/ap_en/1413/subview.do, you can exclude Korean Airline as it only departs from T2 at ICN:

With some airlines, the flight number gives away whether it's a code share.