Re: "My question is, what does the battery replacement warranty cover? Can I claim for this?"
iPhone Repair & Service - Apple Support
says:
"Our warranty doesn’t cover batteries that wear down from normal use. Your product is eligible for a battery replacement at no additional cost if you have AppleCare+ and your product's battery holds less than 80 percent of its original capacity."
Batteries - Service and Recycling - Apple
says:
"Batteries of iPhone 14 models and earlier are designed to retain 80% of their original capacity at 500 complete charge cycles under ideal conditions. Batteries of iPhone 15 models are designed to retain 80% of their original capacity at 1000 complete charge cycles under ideal conditions. Actual battery performance depends on a number of variables, including how iPhone is used and charged regularly. The one‑year warranty includes service coverage for a defective battery, in addition to rights provided under local consumer laws. If it is out of warranty, Apple offers a battery service. Prices and terms may vary."
All rechargeable batteries have a limited lifespan and may eventually need to be serviced or recycled.
For iPhone: iPhone Battery and Performance - Apple Support
Seems battery life always varies with how different people use their devices, and the settings they choose.
Apple Support has an article online (link below) about Maximizing Battery Life and Lifespan
Batteries - Maximizing Performance - Apple
All the best :-)