Rendered timeline/files disappear when I re-open a project

We have 2 computers at the office. One is a Mac Studio and since it is faster and stronger, a lot of times we use that one to render timelines, generate transcripts, export large videos, etc. Other people need to use it I can't edit it on there, I need to take it back to my laptop, a Macbook Pro. 

Here is the issue: For some reason, rendering on the Mac Studio desktop and then trying to open the same project on the same hard drive on a different laptop, does not work. It works for others though. 

It will be a completely rendered timeline in the project on the Mac Studio. But when I eject it and immediatly connect the hard drive to my laptop, the timeline is not rendered and I need to render it again on my laptop. 

Why does this happen/is there a fix? 

I have checked and made sure that under the scratch disk settings, the Video Previews and Audio Previews are in the "Same project folder"...I even tried creating a custom folder for Video Preview and Audio Preview files. When I did this - it completely made it worse because even on the same laptop, I have to re-render my entire timeline everytime I re-open the project. So I got rid of the custom folder.