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https://www.youtube.com/watch?v=nHpvlUWvj9U
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https://www.diychatroom.com/threads/safe-to-open-basement-stairwell-wall-load-bearing.678487/
I read somewhere in one of these forums that having double 2x10s framing the stairwell, with spans less than 16', made of spruce/fir, and having correct hangings of perpendicular joists, does not require additional support -- hence the wall is not load-bearing. Lack of top-plate, and in some places (the back corner I haven't removed yet) the vertical studs aren't even in contact with the double 2x10s (there for something to nail to vs. structural).
The wall you are taking out looks like a partition. Your floor joists are being supported with hangers by the (2)2x10 trimmer, and that trimmer is supported with a larger hanger by the (2)2x10 header, which in turn is supported by your main girder and the wall on the other side. The size of all these members appears to be adequate. An engineer or a building designer who knows how to calculate gravity loads could confirm that the members are indeed adequate. Nice house.