The Video Mode is still 25fps. Video Mode is the native format of the timeline. It is not overridden by the Export screen. The Export screen is an interpolation of the Video Mode, with all the problems that come with interpolation, including stutter. Video Mode is set as follows:
Ideally, the Video Mode and the Export screen will have the same settings. If not, interpolation and potential problems will happen. In the case of the drone video, frames are being dropped to get it down to the 25fps timeline rate (Video Mode), then frames from the 25fps timeline are being duplicated to get back up to the 29.97fps export target. This creates stutter.
Unless the files straight out of the two devices are the same frame rate, one of the two videos will be choppy (assuming 1.0x playback speed) because one video must be interpolated to match the other. That means dropped or duplicated frames which create stutter. The files you currently have are not frame-rate compatible with each other.
A workaround is to slow down the faster video (the drone) to match the frame rate of the slower video.