Is it possible: a linear surface tangent to a face?

Thanks for the answer, Robert!

In my case the reference spline on the datum face can't be planar, unfortunately:
the target surface must be formed by a STRAIGHT line travelling along the profile and TOUCHING the datum face at each point of the path.

This is required by the manufacturing process (folding sheet material, cutting foam with a hot wire).

Thanks anyway)

The model I made is basically the same as what Roger-Marie Couture posted. The only difference was how the base spherical model was split.
- Roger created a six point spline passing through all of the points.
- I created a Curve Through Reference points using the four end points from the layout sketches.

I've attached an image showing how the curvature of the resulting spline/curve varies between the two methods.
The gray model is Rogers with the spline. My model is green and uses a curve.

I can't say if one is a better method. The end result is pretty much identical. If there is a difference, then it may only become apparent when the data is sent for production. CAM software can often discover some very odd issues in models which are otherwise invisible in CAD.

Make use of the Zebra Stripes display option to evaluate the final surfaces.
A SW2017 model is attached.

Like this?

We can not speak here of sheet metal bending but forming because the shape is spherical. It will then be necessary to model a solid anyway. The foam model is easy to perform since the straight wire can follow the curve 2d and the spherical surface. When modeling to ensure the tangency of the surfaces on all the points, smoothing is necessary to smooth out "tangent with the surface". Your smoothing does not allow the surface tangency. For this one must obtain a surface whose border in spline 3d will be smoothed with the other profile See the function "Restrict surface." If you have SW 2018 see the attached file. It is better to check if we can thicken the surfaces once sewn and even better evaluate the results with a merged symmetry.

Even by increasing the number of points of the spline, on this picture ( fil chauffant 4.jpeg) we see that the tangency is normal to the spline of the spherical edge while the guide curves (linear segments) are parallel to each other and perpendicular to the plane surface. What makes imposssible perfectly smooth welts in my opinion. ("zebrures 2.jpeg).
Sometimes you have to sculpt shapes to get an aesthetic smoothing! Bravo for the sculptors but a pity for the heating wire! Do it with a A 3 axes CNC with a ball nose

The perfect zebra of the image "zebrures 4.jpeg" are obtained with the same edges but with a smoothing without guide curves therefore unrealizable to the heating wire!
Make the matrix with an STL file on a 3-axis CNC with a ball nose drill