It's just the two front sprockets which need replaced. The teeth are worn down, and would damage any new chain.
I have to ask the same question as
JohnDThompson Are you certain that your rings are worn? On modern chain rings and cogs they do a lot of sculpting on the teeth to make them shift better. And there are many teeth that are unique in their shape. You might can go to the website of your cranks maker and maybe find a pic of your crank when new and compare.
Also the chain is way harder than the rings. It'll not be damaged by the rings other than if your rings are worn you won't get as much life out of your chain. But you'd still get a lot of miles out of it. So if low inventories are a problem finding something. Just ride on with the new chain. Eventually something will be there.
Typically if your rings or cogs are worn, then they'll show that by letting the new chain skip over them when you start to put some power into them. Though you still have to eliminate some other causes unless you just first want to spend money for new rings or cassette.