I'm filling this bug report just to add more information about the bug, since I've already mentioned it in the SciCraft Discord.
So basically, when a Carpet player is mounted in a minecart on a flying machine, it will not always load chunks while the machine is moving. After experiencing this in a server I've been trying this multiple times in singleplayer and it doesn't always happen, but sometimes the Carpet player stops loading chunks after a while or at the beggining.
I've also recorded a video using your loaddisplay scarpet app to illustrate the loaded chunks: https://streamable.com/1pajmo

fabric-carpet version: 1.15.2-1.3.9+v200206
carpet-extra version: 1.15.2-1.3.9
Fabric version: 0.7.8_build.189

EDIT (28/11/2020): Haven't tested this in a while, will try to reproduce it again Soon™.

That's helpful, thanks for that.

that seems to be fixed in 1.17 due to how entities are handled. That would need re-confirming.