Thank you, Martin! So you are using the built-in add-on Curve Tools to measure the length on the Bezier curve with the help from the Shrinkwrap modifier.
There are 3 concerns with this method:
1) It is hard to tell whether the measured value is accurate or not, because the Shrinkwrap modifier does not guarantee that the curve is actually going through the shortest path between points A and B. So the measured length may be an overestimation over the actual length.
2) Before applying the Shrinkwrap modifier, the length = 0.328139 m on the following screenshot:

After applying the Shrinkwrap modifier, the length = 0.338653 m on the following screenshot:

It is hard to know which value is the correct result!
3) After applying the Shrinkwrap modifier, and then press “Ctrl” + “z”, then Blender crashed twice. I don’t know the reason.