Is there a iPhone 13 manual?

No, there is an iOS 15 manual that covers all models, including the iPhone 13. You can download it with the Books app on your phone, or see this link→iPhone User Guide - Apple Support

Start here: https://support.apple.com/guide/iphone/welcome/ios. You can also download a guide in the iBooks app. It is listed by the iOS version. Just search for user guide.

I need a downloadable pdf version of the ios15 Pro user guide... can't find it anywhere and I can't export the Books version... any workarounds?

I'm afraid not. A long time ago, there used to be PDF versions - but not anymore.