I have my LR catalogue and all of my raw photos on an external hard drive. I mostly use LR on a 2015 iMac but I somtimes use a 2018 HP laptop. As you can see in the screenshots, some folders simply don't exist when I open LR on my laptop. This means that it can't find the files I need to work with. Both versions of LR are the same and I am opening the exact same .lrcat on both computers and the folders and photos are in the same place. I have tried "find missing files nearby" but it doesn't work. It only finds the one file that I manually find.
In the future, So people don't have to download the image you have attached, please use the Insert Photos icon found in the Tool Bar of the Post and Reply text entry dialog window as pictured below. Since you Can't Edit your original post to remove the Attached screen shot Please include the screen shot you attached to a new reply to this conversation by clicking the Blue Reply button under your original post and use the Insert Photos icon in the tool bar. The Insert Photos icon is this one in the Tool Bar.
It is not so much that you are using two computers to work with the exact same catalog on the one external hard drive. The issue is that you are working with two different Operating Systems. The two OS treat hard drive identity's differently, MACOS as names, WIN OS as Drive letters.
This leads to possible confusion. Erratic behavior.
This leads to a more complex Folders Panel
This leads to broken records as to folder and image locations.