The only real shortage of 16ga. shells is in buckshot loadings. I can find plenty of #6 or #8 shot ammo if I look for it. Certainly less common, but you even find it at some Walmarts.
However, finding buckshot in 16ga. is even harder. Back before all this current mess, I lucked out at UNAMMO and scored some. I'll check there again next time I'm looking for some. I've occasionally seen a couple boxes on the shelf at Cabelas', but not regularly.
16ga. shotguns can be a real steal for this perceived shortage. My own 16ga. is a double-barrel coach gun I bought for a mere $100 a few years ago at a gun show from a walk-in. It is basically my designated give-away piece to hand off to some cohort or ally who is not only unarmed but mostly untrained. Something nearly anyone understands how to use with a minimal amount of instruction at the moment of emergency.
Historically, there were only 2 buckshot loads ever widely offered in 16ga., and those were 4buck and 0buck. Today, for whatever reason, 4buck seems the most likely of the 2 to be found. But obviously (to me anyway) 0buck is the one you want.