Upvote:1
On 3/8 ET707 departed 9.33pm from B47, i.e. two minutes early (see https://flightaware.com/live/flight/ETH707/history/20230308/2045Z/EDDF/HAAB) This is normal variation, so the flight was "on time" for all practical purposes.
The gate closing time isn't documented anywhere but it's almost always printed on your boarding pass. I suggest taking a look there. For most US airlines it's 15 minutes before departure (9.20pm in your case) but many other airlines keep it more flexible depending on gate and terminal conditions.
What was your incoming ? Eurowings 947 arrived 8:38pm (on time) and Lufthansa 939 arrived at 6:20pm (20 minutes late, but plenty of time for connecting).I don't see any "late arrival from Manchester".
If this was booked as a single itinerary with EW947/ET707, that was indeed a tight connection but both flights appear to have been on time and the connections seems doable. Frankfurt is large but that's all in Terminal 1. Since the UK is not in Schengen, you would not have to clear passport control either.
What gate did your Manchester flight arrive at, what time were you out of the plane and What time did you arrive at gate B43 ?