Focus plane in front of lenses

I see conflicting information.

As intended by the lens designer, is the focus plane in front of a lens flat (meaning focus off-center is farther away from the camera) or is it convex (maintaining same distance to camera, or something in between)?

For an ideal lens, it is perfectly planar. But for production lenses, these are varying degrees of imperfection. Sometimes the depth of field is large enough that the curvature is not significant in the final image, but sometimes that curvature is quite pronounced. This leads to lenses being referred to as having "field curvature."

I guess that "in-between" is the best answer for reality, but they are intended to be flat

Ideally photographic lenses have a flat field. Macro lenses are very good for this, having very flat focus planes. For lenses with a curved field, usually it is slight. The "plane" of best focus can be curved in either direction. Some lenses, like the EF 20mm f/2.8 USM have the corners coming into best focus a bit closer than the center. Others like the EF 28mm f/2.8 have the corners coming into focus further away than the center.

With most lenses field curvature isn't much of a problem in most scenes, but when photographing a completely flat subject straight on, stop down to f/8-f/11 to minimize the issue by using more depth of field and maximize sharpness.

uOpt wrote in post #14848387
I see conflicting information.

As intended by the lens designer, is the focus plane in front of a lens flat (meaning focus off-center is farther away from the camera) or is it convex (maintaining same distance to camera, or something in between)?

Remember, a camera sensor (or film) is not a 'point'. The plane of focus is ideally a flat plane which is parallel to the plane of the sensor (focal plane), so 'distance' is between two parallel planes.