Share sheet from a tab on i*OS shares a Markdown link and so includes the title and URL, but you can configure this in the share sheet settings in the app. But it is always just one at a time.
If you want to retrieve say the last current tab or all tabs, on the Mac, there are quite a few AppleScript examples online for various browsers. Utilising TextExpander, Keyboard Maestro, or even Alfred can give you a way to access that in any app. Drafts doesn’t currently allow external scripts to be triggered from actions, so you probably need to look at a third party tool for that.
The sharing from the browser to Drafts on the Mac might also work for single tabs, but I’m not able to check that just now.
Hope that helps.