When doing the area measurement manually, the standard method of creation is a curve that is connected via gradient connections rather than a spline. In case you are using a spline, can you let me know your workflow for this?
When doing the measurement automatically, you have the option to either turn “snap” False which enables straight connections between the points or to turn “snap” on True which uses the same gradient connection process as the manual measurement.
In case you want to work with a spline for the automatic measurement, you could create a spline and subsample it to have e.g. 1000 points and use all those points as input with “snap” on False. This will approximate the original spline (the more points used, the smaller the error)
Hope this helps!