How to search for text within an app?
Apple doesn't index every bit of text in every app (that's not their own app, like Notes).  It's up to the app developer to add a search function or to explicitly make their content searchable by Apple.  The latter part is becoming more popular because the iOS Spotlight function is getting better.

For example, if I do a Spotlight search on my iPhone for 'plex', the results include the Plex app that I have in addition to several emails I've received from Plex.  These emails are in the Spark email app, so that means that developer added the code to make their content available to Spotlight searches.

At this point, it's hit-or-miss if your app supports this.  Often, the developer will indicate if this feature is available on their iTunes page.