I have several bookmarklets saved as favorites in Safari on iOS. They are "pageless" in the sense that they don't do anything to the page I'm on, and I don't need to be on a page to run them. I launch them as bookmarks from a Safari new tab page, and they present a pop-up dialog box. I type a query, and they string that query to a URL and open it.

Here's an example bookmarklet that let's me search terms on Naver, the Korean version of Google:

javascript:var s=prompt('Naver search');if(s==null){}else if(s==''){alert('Please enter search terms')}else{location.href='https://m.search.naver.com/search.naver?query=' encodeURIComponent(s);}

I'm trying to reproduce this in a shortcut that I could then launch from a lockscreen widget or a homescreen icon.

I was hopeful I could just add the bookmarklet to the homescreen the same way you add any other bookmark, but no luck. Meanwhile, I am struggling to modify other people's shortcuts to get the behavior I want, but again, no luck. This feels like it ought to be simple but maybe I'm just too dumb.

What I want:

1. Press a home screen icon
2. Pop-up dialog box appears, asking me to enter a word or phrase.
3. That word/phrase gets added to a URL in the right location
4. That URL is opened in Safari