Add this moment when you enter an URL in a Paragraph-block there is only one setting: Open in New Tab. I like to be able to add settings such as Link Style. That adds a class to a link.
It cannot be done, no API currently exists to add what you want to add.
If we look at the component that implements this:
InlineLinkUI wraps a component that wraps the
URLPopover component, and places a child component inside it which is how the new window checkbox is added. No slots are present or hooks for intercepting this.
Judging from what you want to do, I don't think this is the intended path forward. Instead, build a block, or a new inline block. You can also open an issue on the Gutenberg GitHub requesting the feature