They retracted the gear after the first landing attempt. I suspect they either missed it on the teardrop or had secondary hydraulic failure and no time to do a gravity drop. I would err on the side of crew error because there were clear signs the hydraulic systems were functioning (thrust reverser and that they could retract the gear in the first place). Hydraulics don’t fail instantly and one engine was spooling still on landing.
That's why EASA says put the plane down if there’s a strike on approach. Ryanair 4102 is a good example of a close one there as a reference.
Yes, if you view the footage of the bird strike on first approach you will see the landing gear is extended.
ETA: The primary footage is hard to find now that the topic is so saturated, but there is a specific clip from a close vantage where it is highly visible. I'll include a link if I can find it.
That's why EASA says put the plane down if there’s a strike on approach. Ryanair 4102 is a good example of a close one there as a reference.