Canon EOS 200D 11 recorded footage over 5 minutes long is not uploading to my computer?

Iare probably has the answer. You thought the camera was still recording but it stopped recording at the 4 min mark. Therefore no files exist beyond that 4 min mark.  Thus there is nothing to upload.

Can you actually see video footage in the viewfinder or camera screen when you play the longer 'recording' in the camera?

like most still image cameras in movie mode, the max video file size is 4GB.  unlike most similar cameras this model does not automatically stop video mode when the max file size is reached.  so you think you are still recording when in fact it is not.  you should be able to get close to 8 minutes of video when recording at the best resolution setting.  if you need longer recording continuous recording time, then you need to reduce the resolution.  however, the max continuous recording at any setting is 30 minutes.  this is not a camcorder, many of the camera features do not work when in movie mode, the video feature is just a bonus for occasional needs.

I'm confused!  You wrote "after that the clips seem to be completely nonexistent. ", and then "They are still on my camera".  Are you saying you can see the files when you use the camera but your PC can't see them?

Still cameras that shoot video have short shooting-time limits. 

If you need reliable video recording, use a camcorder.