I've looked a little further into this, and those file paths (/var/folders/) look like they store the temp files and cache on MacOS. What is likely happening is that the textures are stored in that temp directory, and since temp files are volatile and subject to change or deletion, it leads to the textures not being detected consistently, and which is why you weren't able to find them through a search.
One way to prevent this from occurring in the future is if you use the Resource Collector in Twinmotion's Edit menu. This allows you to easily create and save a folder containing your Twinmotion file, as well as all of your textures, so textures won't be lost because they're being stored in the temp directory.
I hope that helps.
Best,
Raghib