iPhone battery Performance Issue - Need Help

From last 2 days, my iPhone 13 battery's performance is getting worse. It automatically turns off while using it whether using different apps such as scrolling Instagram or doing another task it suddenly turns off and restarted. It's draining so fast like just showing my battery percentage from 70% to 10% instantly.

And it's happening again and again. Currently, my iPhone battery's power capacity showing me is about 64%.

I contacted Apple support; the support assistance told me to replace my iPhone's battery after it was diagnosed with it virtually while on call via screensharing. But it cost me around $100 onwards.

Should I have replaced my iPhone's battery from an Authorized Apple care near me or try to find battery solutions in other markets? Bcoz replacing battery from an authorized Apple care is too expensive. Is it worthwhile for me?