To get equirectangular texture mapped correctly it is usseful to know distance of the camera (that took a shots) from a ground. Usually it is about 1.5 - 1.7 m.
This should be a distance of floor face from object's origin, because the origin represents the place of real camera and all pixela of equirectangular texture are like exploding sphere into all directions from origin location.
It is quite useful to position also Camera object at Plane's Origin. Lock position at X=0, Y=0, Z= Plane's Origin and enable under 3Dview side Properties panel (N) View tab > Camera to View.
In Shader editor > World set the same equirectangular texture. Now they should match from Camera view.
With Plane selected switch to Edit mode and start to reconstruct environment ...
- Or if you know some distances you can ensure with those. Like if you know size of floor, set that in edit mode and by moving this face along global Z axis you can adjust position to match with a texture.
- and sure ... you have to use Environment texture node (not Image node) ;)
- You don't have to use a Camera setup described above, you can directly extrude faces in 3Dviewport, but gives you nice overview what is where.