Your observations indicate three Mission Control behaviours in the current macOS version.
First, the names shown for full-screen applications in Mission Control are dynamically generated. In Safari, for example, the displayed name can correspond to the website, while Mail can display an inbox name. This makes it more difficult to identify the required window. You have also observed that this behaviour does not occur under Tahoe.
Second, when Mission Control is initially opened from a Desktop, full-screen applications are displayed as names without thumbnail previews.
When the pointer is moved to the top bar, Mission Control changes to displaying thumbnail previews.
This reduces the available vertical space for the Desktop windows, and the windows then rearrange. The attached video shows this occurring during the transition.
Third, when a full-screen application is selected, the Desktop icons first become visible before the application switch takes place.
This results in a delay of approximately one second. Changing Reduce Motion did not change the observed delay.
The setting "Automatically rearrange Spaces based on most recent use" is disabled, and toggling it did not change the behaviour.
Toggling "Group windows by application" also did not change it.
Testing with a new user account did not change the behaviour either.
The window rearrangement therefore occurs specifically during the transition from the initial label-only presentation to the thumbnail-preview presentation.
The delay when selecting a full-screen application is a separate behaviour involving the Desktop contents becoming visible before the application switch completes.
These observations, together with the attached video and the comparison with Tahoe, provide specific details that can be included when reporting the behaviour to Apple.
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