How can I get a word count in iPhone notes app?

Although I do implement Shortcut solutions on macOS, I don't on iOS or iPadOS, so here is an opportunity for you to post the tested Shortcut code here to count words in Notes so others can benefit.

That iOS Notes app was not implemented to count words. You need to select the words that you want to count in Notes and then copy to the clipboard. Next, you open Pages for iOS to a new document, and you paste from the clipboard. Select the Pages content again whose words you want to count. While that is still selected, click the ⋯⃝ tool in the menu bar and from that resulting menu, select View Options : Show Word Count.

A badge with the Word count for the current selection will then appear bottom-center in the Pages document.

Pages for Mac, iOS, and iPad have subtle implementation differences. Reading the wrong docs can send you astray.

Unless the idiosyncratic behavior of Pages is part of the goal here, there is actually simpler way to get word counts in Notes—if it is an ongoing need.

Using the Shortcuts app, make a three-step shortcut: (1) Receive Text input from Share Sheet; (2) Count Words in Shortcut Input; (3) Show Result. Then in the Details section, make the shortcut available in the Share Sheet. Finally, Share the note (or select the text in question, and choose Share...), activate the shortcut in the Share Sheet, and receive a word count.

Fair play...

This is the most basic of implementations—really more of a proof of concept. It does not detect errors, let alone provide helpful feedback when something goes awry. Further, while it works on iOS, I do not think it works unmodified on MacOS. (Not tested on iPadOS yet, but I suspect it works fine.) Perhaps a combination of your shortcut and mine would be cross-platform...?

Word Count Shortcut for iOS