To justify my stance, in a long term survival situation slings are for low risk low reward hunting. With even moderate practice they become very high calories per resources and time invested while your doing something else. Aka, if you’re collecting firewood and see a squirrel, vs specifically looking for squirrels. That’s still true if you’re missing 95% of the time.
Plenty of active bow hunters are around to tell you how long that takes to learn. Unfortunately, manufacturing arrows and replacement bows takes significant effort. Atal are generally worse than bows, but vastly easier to manufacture and maintain.
As to ammo it’s very much possible to find good ammo that’s 50 years old. Depending on specific ammo to still be good in 50 years is a very different thing when you can’t depend on climate control. That’s not a concern at 70+ but a 25 year old presumably has a longer time horizon.
As for atal or sling, unless you've been practicing with these since you were a child, I think you'll sooner starve to death than score yourself a single meal. The cultures which used those tools had people practicing with them for years before they were useful with them. A sling is easy to make, I encourage you to try it out. I used a pair of shoelaces I bought at the grocery store for $2. It is not easy to even get the projectile flying in the general direction you intended, so if you try this make sure you're far from any buildings or bystanders...
(But really, I recommend buying some canned food. It is unlikely any infrastructure collapse would last more than a few weeks. Any scenario where you have to hunt for food at all, let alone for years, seems exceedingly unlikely.)