Fixing: "There are no devices registered in your account" without a Lightning cable Xcode 11.0
I don't have a USB-C lightning cable with me, which seems to be a direct requirement to connect my iPhone to my Mac.
Is there any way to solve this issue?

You'd need to connect and pair your iPhone to your Mac at least once before you can perform wireless debugging.
If you do not have a USB-C to Lightning Cable cable, you'd need to either get one or use a USB-C to USB Adapter (like this) or a similar hub.
The iPhone (or any iOS device) needs to be connected physically to the Mac and you'd have to manually Trust the iOS device before it could be paired with Xcode. This security reason is why you'd need a cable to connect the iPhone in the first place, and there is no way to work around it wirelessly.

There is a secondary error that says that no profile was found for my bundle ID, but I'm pretty sure this stems from the previously mentioned one.

You can resolve this by going to Xcode Preferences → Accounts and add your Apple ID. If it is already added, you can try by removing and adding it again.