Help determining if wall is structural that runs under old basement stairs

I know this is a question that is extremely tough to answer online, but I am just trying to get a general sense of the situation. We are putting in a 1/2 bath in our basement and when I opened up the ceiling, it turns out that old set of basement stairs used to come down straight through that area. The old opening has double joists on both sides that run to the load bearing wall to foundation and header on the one side we can see, the other side is buried in the drywall that isn't coming down for the project. Blocking is bridging the 32" opening. Above this area is now a pantry and coat closet.

There is an 8ft wall that has a 47" closet door opening with 2 studs on either side of the opening in that wall. That wall has the blocking perpendicular to it, which is shown below. That wall is also going to move out and will be located on the other side of the double joists, so the blocking will not be running over it.

I want to know if this wall has any structural components or is simply a closet wall? The wall had no electric or plumbing. I have not been able to get much help or anyone interested in coming to look at the project.

First Pic of old stairway


How that closet door wall looks



Drawing Notes:
- The blue closet wall will be moving to the left of the double joists (black)
- The hallway (where the green text is) is finished so I can't see how the old stair's header is siting. The joists do cross the the load bearing wall when I trace it with a stud finder in the ceiling.
- The load bearing wall runs the length of the basement and on the main level (one story house) there is a wall on top of the it that runs the length of the house too.
- The double joists on the left runs through the X, which on the main level is that load bearing wall and a perpendicular 8ft wall meets there as well. That wall runs on top of a portion of the closet wall in the basement by about 2 ft or so.
- There will be a 28" door put into hallway wall, but I don't think that will make a difference.




I tried to color code the pic to match the drawing

 

You're talking about the white 2x4 that had the sliding closet door? At least from the part we can see, that's definitely not a bearing wall. It wouldn't be able to support much of anything with a 2x4 in that direction with 4' between studs.

The doubled joists are the ones that need to be supported on either end. You stated one side of the double joists are supported by the blue wall at the top of your drawing with the X. Perfect. If you can find where the other end is supported, you'll be all set.

 

The other end lays on the foundation, so it sounds like I am good. Thanks for the help.