Many thanks for coming back to me on this.
In answer to your question, yes, that is correct - these are local files that are opened in a particular order, but on subsequent app launches, the order is lost and they open in a random order.
To add some detail re: "local files": My libraries are normally stored in an iCloud Drive folder. After reading your message, I created copies of my libraries on my desktop - i.e. stored locally on my laptop, not in the cloud - and repeated the whole process. I got the same results. So to be 100% clear, I get the same behaviour both when the libraries files are stored locally on my laptop, and when they're stored in iCloud Drive.
I also tried naming the libraries with a number of the start, however the file naming seems to have no impact on library ordering either.
The only way I have found to reorder the libraries to date, is to close them all from the left panel, then re-open them one-by-one in reverse order (i.e. the library I want at the top should be opened last). This works until the next time I need to open / reload the
draw.io app.
Does this give you the detail you need?