You can of course rebuild the floor upstairs so that you can properly support the weight and transfer it to the central post in the staircase. This should not be a problem if you contact a manufacturer of spiral staircases. However, I guess you might not want a staircase from Weland in the house?
Alternatively, you can seek support in the ceiling instead and hang the joists from the truss, which may need reinforcement.
You'll have a small issue with temporarily supporting the joists while the staircase is being installed, and it's not a big deal, judging by the picture, as long as you don't nail too much around the stair hole.
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The Builder