Comment by HSO

Now I wanted it for myself and just made it. So at least I can confirm this works.

Only difference is I don´t actually use the sharesheet much so I do it with clipboard content: Step 1. Take screenshot or copy text. Step 2. Make a request to AnkiConnect and have it create a new card with clipboard in Anki.

Works flawlessly on Mac/Desktop but if you want to do it from mobile devices, you have to muck around with network permissions. Too much for this evening but this alone opens up possibilities.

Thanks for the stimulating question! :)