Apple - Can you listen to music using AirPods without an Internet connection?

You don't need an Internet connection at all.

Per the Technical specifications under System Requirements:

• iPhone and iPod touch models with the latest version of iOS
• iPad models with the latest version of iPadOS
• Apple Watch models with the latest version of watchOS
• Mac models with the latest version of macOS
• Apple TV models with the latest version of tvOS

It makes no mention of an "active Internet connection." You can play stored music without one and I've controlled Siri on many occasions when my ISP has had an outage. She obviously can't do lookups, but will respond to local commands.

Can you listen to music using AirPods without an Internet connection

Yes.

Does one need Internet connection to use Siri?

Yes.

You can listen to locally stored music just fine using AirPods. AirPods does not need Internet connection to function.

Sure, the AirPods don‘t need an Internet connection.