I recently came across this thread on TidBITS looking for an app for scanning and OCR. The solution comes with every iPhone and iPad: Both the Notes and Files apps can scan and perform OCR automatically. Open Files and look to the top of the sidebar and tap the circle ellipses then “Scan Document”. The scanning app will autodetect each page and snap the scan for you then wait for the next. When you’re done tap save. Text detection is automatic and can be searched for within the Files app by opening the PDF.
Alternatively, using the Notes app, open a new or existing note and tap the camera icon in the toolbar to bring up the scanner menu. Choose the option to Scan Documents.
The difference between these two methods is that documents scanned into the Notes app are also indexed by Spotlight on the iPhone and iPad, and so are searchable both within the Notes app and just using the systemwide Spotlight feature. PDFs created by the Files app are not searchable in Spotlight.
It’s also worth noting that this is also a feature in the same apps on the iPhone. Additionally, almost any app can take advantage of what is, essentially, system–wide document scanning. The Notebooks app that I have been using recently allows for scanning documents, and importing with the OCR. So does Apple’s default mail app. And I’m sure there are others.