Can I use Continuity Camera with Siri on my iPhone?

Sort of, yes.

You can go to Settings ➜ Sound ➜ Output & Input ➜ Input, and click on your iPhone there to set it as the microphone.

To then to use it with Siri, you'll need to click the Siri / Apple Intelligence icon on the Menu Bar, and then on the Microphone icon on the right side of the search field that appears. You can then talk to siri through your iPhone's Microphone.

It won't directly respond to Siri requests otherwise though.

Not sure what you mean.

You access Siri by caling her up, and asking something. "Hey Siri, what's the weather like?"

It has nothing to do with the camera. The Camera is not involved with Siri.

If you mean can you use Siri on your iPhone will using contnuity Camera with a Mac, then no, since the iPhone is in use and you have no access to it, but if you are using a Mac, then you have access to Siri on the Mac.

If that is not what you mean, please clarify what you are trying to accomplish.

Yes. You can use the function wired or wirelessly.