Does my iPhone 13 need antivirus protection?

Absolutely not! Any apps or advertisement that you see that claims to offer protection is a complete scam. There is no app that is capable of scanning your iPhone as there is no access to the file structure. For that same reason, there is not virus that could also gain access to the files structure to embed itself.

The one exception is for the case that a user had jailbroken their phone for some reason. This is an intentional action and not something that is done by accident and will eliminate any security protections. There is no support for a jailbroken device.

No. A non-jailbroken phone cannot be hacked, get malware, or a virus.

And if you don’t know what “jailbroken” means then you don't need to worry.