Looks like we are missing a redraw call in some cases, previews are loaded but for some reason default preview icon is shown, as soon as you move mouse cursor all those previews get updated. It is probably related Asset Database because it is connected to Reimport/Reimport All. Also it is related to HDRP - as soon as I remove HDRP package it not reproduces.
Not reproducible on a new URP or HDRP projects

How can we reproduce it using the example you attached
1 Open attached project
2 Do Reimport All
3 Go through All Materials, All Models, All Prefabs
4 When you select All Materials - previews are not loaded, you need to move Mouse cursor over that tab or click on the tab if cursor already there
5 If it stopped reproducing - do Reimport of Assets folder and try steps 3-4 again
Attaching repro video (in comments)

Actual results: Previews in All Materials aren't shown for some materials until you move mouse cursor on that Project Browser tab

Expected results: Previews should be shown

Reproduces on: 2022.1.0a4, 2022.1.0a6, 2022.1.0a9 (haven't checked others)