I don't believe all surfaces can be measured, I see a similar behaviour on my X when trying to lock onto some vertical objects, yet when I pan down to say the carpet, the circle with the dot appears and the "plus" then highlights so you can add your first coordinate (ie. "Add a point").
While moving around to get that first point various prompts should appear, "Find a nearby surface to measure", a flat square with "Move iPhone to Start" ,a 3D box with "Continue to move iPhone", when it gets to a suitable surface a circle with a dot appears and the "plus" button then highlights. While you continue to see the circle/dot you can add additional points to create "lines" for measurement, once done the right hand button allows an image to be captured of the progress which is stored under Photos.
With regards to the level, that has to be "tapped" to select, once done you can then place your device on a suitable surface to measure (either edge on to display "line" and degree angle or flat to show "two circles" and degree angle).
Anyhow, that's how my X with the Measurement App appears to function.
Hope the above helps.