How to reproduce:

Open the attached "IN-153731_repro.zip" project
Open the “Main” scene
Select the "GameObject 1" instance in the Hierarchy tab
In the right-side Inspector tab, click the circle icon next to the Prefab field to open the Select GameObject window
In the “Select GameObject” window, click "GameObject 2", then "GameObject 1", then "GameObject 2" (three clicks in total)
Observe the prefab assigned in the Inspector

Actual result: The first two clicks apply. The third click does not change the prefab assigned in the Inspector, no errors are logged in the Console
Expected result: Every click in the Select GameObject window assigns the clicked prefab

Reproducible with: 6000.0.7f1 (7dd95c051e11), 6000.0.84f1, 6000.3.25f1, 6000.6.3f1, 6000.7.0b1, 7000.0.0a1
Not reproducible with: 6000.0.6f1

Reproducible on: Windows 11
Not reproducible on: No other environments tested

Workarounds:

Switch to the Default Editor layout (Window → Layouts → Default)
Assign the prefab by dragging it from the Project window onto the field instead of using the picker
Close and reopen the Select GameObject window, assigning only one prefab each time it is open
Keep the component order consistent across the prefab variants you cycle between

Notes:

The two prefabs cycled between have different component sets and order: "GameObject 1" has a Box Collider, Mesh Renderer, and Capsule Collider, while "GameObject 2" has a Capsule Collider and a Box Collider, so a different control sequence is drawn in the Inspector for each
Reproduction depends on the Editor window layout: the issue reproduces with the layout that ships with the attached project and does not reproduce with the Default layout, on the same project and Editor version
The layout in the attached project contains two Inspector windows; the issue reproduces in the right-side Inspector and does not reproduce in the other one