At what percentage should I start considering a battery replacement for my iPhone 13?

Apple recommends replacing at 80%, but if they may not actually replace it until the battery is at 79% or less.

I had Apple replace the battery in my phone at 81%, but they were reluctant to do this for some reason that I do not understand.

When it drops to 79% or lower. Hope this helps!

Apple replaced mine at 82% with no push back when I reported that the phone was shutting down unexpectedly. I suspect that, to some degree, it depends on the store.