Apple Notes: How to OCR and search both pasted screenshots and the associated markup text?

I thought my use case was a simple one, but I can't find any note-taking app that supports it:

I want to be able to (at least on my iPad):

1. Paste/Import in a screenshot,
2. mark it up with my notes using the Apple Pencil, and
3. be able to search by both the text of the screenshot and my notes

In Apple Notes, while in regular text mode, you can paste in a screenshot. The text in this image is searchable! How awesome! However, if you tap on it and go in to markup mode and add some handwritten text notes, those are NOT searchable. Bummer.

Alternatively, you can start in drawing mode and paste your screenshot in there and mark it up with your handwritten notes. Your handwritten notes are now searchable! How awesome! However, now the text in your screenshot is not searchable! Argh!!

Why can't we have both? It seems like such a simple use case, just want to be able to take screenshots, mark them up with notes and search the text of both the screenshot and my notes.

Is there something I'm missing? Is there a way to do this in Apple Notes or any other App? (Tried GoodNotes 6 and for pasted screenshots it searches your handwritten notes, but not the text of the screenshots)