First, data vs transforms. When you edit things in edit mode you are affecting the data. When you edit things in object mode you are creating transforma. Take the default cube, tab into edit mode, in mesh overlays check edge length. You will see that all the edges are 2m. Tab to object mode and press n to bring up n-panel(technically called the sidebar) on item tab at the bottom you will see that all dimensions are 2m. Scale by 2(press S then 2 then left click). Now the dimensions are 4m. Tab into edit mode and the edges are still 2m. Tab back to object mode you will see that the scale is 2. That means it is multiplying the data by 2 on all axis. Then apply the scale. Scale becomes 1. Now when you tab into edit mode the edges are 4m. When you apply any of the transforms it changes the data.
Second, to answer your question. What gets changed is not only the curve and handle length, but the radius is also multiplied by scale. This is what’s causing your problems. You can go to edit mode, select all control point(also called vertices) of the curve and on the n-panel hold alt when you click in the radius field. Change it back to 1 and press enter. For people using emulate middle mouse button just click in the field, enter number, and press Alt+enter.
