Can iOS NFC reader display notes? Can the native iOS NFC reader be used for simple notes?
I can program all tags with links, actions etc. As soon I store a simple text the native reader just won't read the tag.
Yes - you could embed the notes in a database and trigger display from the encoding on the tag.
If you’re writing specific content into an NFC and asking how the OS handles arbitrary items, we might need a substantial edit to the question and possibly move it to a different site, but many apps do this.
Apple has code ready to run, frameworks, WWDC videos and more on how the capabilities and hardware and software work together.

https://developer.apple.com/wwdc20/10140