I don't think there's any computational way of doing this. The main problem is that whatever computational software you have isn't going to know your true HFoV (how far you rotated), and you can't use the aspect ratio, since it's not a true equirectangular mapping, and you're missing VFoV (i.e., you haven't covered the entire ceiling or the entire floor) for an equirectangular.

While you can load it as an equirectangular, what you've most likely got is something like a 380-ishº cylindrical.

Control points aren't really going to help you other than to straighten stuff out, and you can probably eyeball/drag it faster in the GL preview of Hugin. You do have some tilt and roll issues as well (given the not-straight horizon).

Only advice I can offer is to straighten out everything so your doorframe verticals are vertical using the Drag/Move tab in Hugin GL preview and dragging vertically to adjust pitch, right-dragging to adjust roll, and horizontal dragging to adjust yaw. Then adjust the yaw, so the edges of the image are in the center of the image, and then doing a crop so the two edges (hopefully) meet.

…and I just tried doing this, and it looks like you shot free hand, while turning around with your phone in your hand?, and so you've also got parallax/drift errors that won't let the two sides come together seamlessly…

If you had individual member images that were stitched together, you could realign the individual skewed bits to the pano, but since you only have the whole pano, and stuff is already stitched together, I'm not sure there's any way (let alone an easy way) to adjust for that additional roll/tilt on that one side of the pano to get it to square back with the other side. I mean, maybe you could use Skew in Photoshop or something. But I think you're always going to see the seam.

360s indoors shot without a panohead are usually problematic due to parallax.