Here in the UK, shotguns are relatively easy to obtain, and ammunition is plentiful.
Lawful private ownership of rifles is rare, and lawful private ownership of handguns almost unknown, so ammo supplies not relevant.

Moving to other supplies there are still local shortages of toilet paper, cleaning products and some canned goods. No generalised shortage though.
Turkeys are very commonly eaten at Christmas, and some reports suggest a glut of these birds (fewer large family gatherings) whilst other reports suggest a shortage for some not clearly defined reason.

Firewood is in short supply and expensive. Propane is much less used here than in the USA but supplies seem adequate. I purchased three large portable cylinders each of 19 kilos without problems.
Coal is less used these days, but is readily available.

Our stocking up has been limited to ensuring that we have a two week supply of real essentials (medical, food) in the event we have to quarantine. And we did have to do so once a few months ago due to a potential contact.

Beyond that we haven't seen too many shortages. We buy a lot online, partially due to our remote location. Lately I've been feeling bad about how much of it is via Amazon. No doubt some online purchases, such as a table saw and a miter saw have been to avoid going to big stores (with a perceived higher virus risk). It is amazing what can be purchased online. Heck, I recently bought a 60 inch PTO driven snowblower for my tractor online. Amazing.

TP & paper towels have seen sporadic shortages the last week or so. Costco here has been cleaned out but the closest supermarket to me is fully stocked. Dish soap has also been kind of variable, which seems odd but most of the panic buying doesn't make sense. I live by myself so it's pretty easy to be "stocked up" on most stuff, at least stuff that's not perishable.

Where I live, we're suffering a shortage of personal responsibility and self-discipline right now. C'mon, fellow citizens, show a little backbone!

/end rant

WRT the shortage of dish soap, this might be not very rational panic buying, or alternatively production may have been curtailed.
Many manufacturers produce a range of cleaning and hygiene products, and I consider it possible that production of dish soap may have been limited in order to free up factory space and staff for hand sanitiser production.

Yeah, I suppose that could be. I stocked up a little, not a ton. In "normal" time when there's all the soap you could carry, I tend to buy a bottle when I'm almost out. But now when I find it I usually buy two bottles at a time.

Regardless of prepping mentality or the circumstances, I think it is wise to buy a few more than we need. It saves time and frustration. If you have a pantry or enough space , it is wise to have your own "store" at home, especially for non perishable items like soap ..etc.

Sometimes, you are not in the mood to go out, or the roads are congested for a reason or another, or the weather... etc. There are a million reasons that we should store a few extra of everything. Find a balanced level that is suitable for your lifestyle and size of your family, and I think no one will regret having a few things stashed in the pantry.

During the pandemic lockdown, two of the kitchen appliances broke down. When things eased a bit, I bought TWO of each.

I agree but in "normal" times it's not a big deal to me (with dish soap that is). It gets used at a pretty steady predictable level so it's unlikely that I'll be surprised to run out. But yeah, in this "new normal" I tend to stock up more on everything than I used to.

We never stopped limiting TP & PT in many places here.
(Southeast PA)

No shortages at the local grocery store...