Unwanted re-shuffling of multiple desktop spaces and other challenges

I have been user of multiple spaces for years. Like probably many others, I set up different spaces to keep work in one area separate from others. I use a number of different ways to go from one space to another, but what is very important is that the sequence of desktops remains fixed. That is, if I go into Mission Control and add a a seventh space to a collection of six, I expect that new space to remain Desktop 7 when I open Mission Control the next time. While Mission Control does give you the option to rearrange the order of the spaces/desktops - and I would do that on occasion - I could count on the sequence to remain fixed between visits to Mission Control. No brainer, right?

I never had reason to doubt that this very sensible feature of fixedness was built in - nor even considered that it wouldn't be. That was until about six months ago when I decided to implement multiple spaces on my personal iMac, which then (and still is) running Mojave. I set myself up with 5 desktops, but almost immediately I noticed that none of the added spaces would stay in place. One day the space originally set up as Desktop 2 and then the next day it would appear in Mission Control Center as Desktop 4.

More recently I began to encounter the same squirrelly behavior of multiple spaces on my new work computer. This is a 2019 MacBook Pro upgraded to Big Sur. Prior to this, I had been using up to 16 spaces on MacBook Pro of the same vintage and specs and never had a lick of trouble with spaces jumping around. Not even in Big Sur. This strongly suggests that there is a setting on the new machine that I need to change, but there is nothing that I can find in either System Preferences or in the Finder preferences that even mentions spaces, so it seems I'm a up a creek.

While I suspect that this unasked-for re-shuffling has something to do with the moving windows between different spaces, I haven't been able to figure out what is causing it to happen nor how to stop it. And the Apple support pages make no mention of this issue that I can discern.

At minimum, I need to know the trick to making the spaces stay put.

Thanks for reading this through to the end. I hope it describes my problem in sufficient detail.

Cheers