Siri only has access to first party Apple apps at this time. The APIs are there for developers to start testing, but nothing they make is going to be approved until September.
Every individual app has an Apple Intelligence & Siri subsection in the Settings app that can be individually turned off. Everything is enabled by default at this time.
That said, if you leave Siri AI on for Mail.app and have bills and receipts in your email, that financial data is accessible by Siri. I can ask Siri how much my water bill is and it will pull that info from my email.