A .177 pellet gun will do whatever a .22/.410 will do and not make firearm report.

Um, no. I can shoot birds on the wing with the .22/.410, not with the .177.
I can sluice and entire covey of birds on the ground before they rise with the .22/.410, not with the .177.
I can shoot subsonic ammo out of the .22/.410 that is quieter than the hunting .177 I sold a while back.

There’s a reason I have 2 .22/.410’s and got rid of the .177. Not as useful, but that’s me.

working gun like a Browning BAR sporting rifle won’t hold up under continuous firing rigors.

The FNAR is nothing but a tweaked Browning BAR. And it’s fine for ‘continuous’ firing.
Better mags on the FNAR however.

The FN bolt guns are nothing but rebranded Winchester Model 70’s.

The .223 isn’t legal everywhere for hunting. Here it’s only legal for deer and smaller, and then only with 60+ grain bullets for big game. And from personal experience, I’m still not enamored of the .223 even with heavier bullets.

Much depends on the circumstance of SHTF.
Were I in SA like Leopard, I would likely be more concerned with high capacity than large bullets.
Were I in deepest darkest Alaska, I’d be more concerned with large bullets.

Everybody’s choices are determined by their circumstance and location.
People in Pennsylvania can’t hunt with semi-auto rifles/handguns. Leaves much to be desired.

There is no one answer, one gun or bullet that fits all.
Sad because we all could have saved a great deal of money over the years trying to find that one.