I use PopClip on Mac. Is there an equivalent app for the iPad/iPhone?
I don’t think so. I would love to be wrong, but my impression is that the contextual menu on iOS is extendible only by the system and maybe by the app that you’re in at any given moment.
If I’m right, the share sheet is your best bet on iOS, and then of course you can use Shortcuts, Scriptable, etc.
to a certain extent that would be shortcuts, you can mimic most of the actions in popclip by building the equivalent in shortcuts app and using them through the sharesheet