The previous webpage offers the correct mechanism:

https://www.grc.nasa.gov/www/K-12/airplane/right2.html

Note that in: F = m * dV/dt

F and V are vectors with components in 3 dimensions. Of course the z-axis is of most interest. Drag and vortex effects manifest themselves principally in the x and y axes.

And yes, there's a vast amount of mythology on lift generation in most pilot textbooks.