This issue seems to have started with updating to latest AAO (4.20 b43) and/or StreamDeck plugin (35.02).
When MSFS is the selected foreground application, "Lorby-SI AxisAndOhs" button presses will have a varying response time in MSFS from no delay to no response at all.
If another application is selected so that MSFS is no longer the foreground application, there is never a delay.
This issue is not occurring with other Stream Deck plugins (Flight Deck, Flight Tracker, etc.).