How to get obsidian to show up in the iOS "share tray" for PDFs

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While this is not ideal, you could try to create a shortcut in the iOS Shortcuts app.

I’m not 100% sure on how to recreate this as I am not that good with shortcuts myself and don’t use PDFs much.

This is a good read though: iOS Shortcuts - Share your ideas! - #78 by Felipe
Maybe you could get ideas from it.