Using a regular small pistol primer vs magnum primer
Standard small pistol primers in general have thinner primer cups and less priming mixture than the magnum small pistol primers.
For practical purposes magnum small pistol primers are the same or similar to the standard small rifle primers from the same manufacturer.
Testing reassembly of the firing mechanism of a compact striker fired pistol (Ruger PC9s) using an empty 9mm cartridge case with a CCI magnum small pistol primer (and hearing protection with my cat out of the room), I got dimpled primer no fire. I pulled the bullet from a standard 9mm factory round and dumped the powder: I got positive ignition from presumably a standard small pistol primer.
Luck for me the pistols I reload for (C96 Mauser, Ruger Security Six) have heavy hammers and strong hammersprings and fire magnum small pistol and standard small rifle primers consistently. And they have fired small pistol primers just fine also.
My concern in this primer shortage would be people short of standard small pistol primers switching to small pistol magnum primers or small rifle primers and finding their handgun won't fire magnum pistol or rifle primers due to light firing pin strikes.