It is your expectation of doing this with the notes app that makes this request go from reasonable to… quite strange.
Notes are stored in plaintext (and inside a database, but never mind that), basically not a formal file format. I can’t readily imagine a good storage format that would allow for your use case, and the simplicity of plaintext is quite nice (for sharing/sending it).
So ignoring the specific app for a minute; copying and pasting of images could be pretty neat, but receiving apps would of course need to do some work to handle it. However, it is also not quite as useful as on a desktop - here you have ready access to last added images, and the sharing functions.
But that e.g. Android has this is news to me, because at least everyone i know seems to be posting screenshots as if they didn’t even have “save image as”. What does it “usually” work with?
Also, please decide on one thread to post about the same thing in. Maybe even ask for a merge.