I Experience this same issue. A copy and paste will paste something I previously copied repeatedly no matter how many times I re-copy and re-paste. Though I have found a solution that while a big time consuming, does work.
FForget you have a copy option. Use "cut" and if you are in a browser, or near one, paste it into the irk bar. I've been doing this a while pre-this bif, as the only way I found to remove styling to be able to "paste as plain text".
By pasting in the URL bar you can see if your cut/copy worked. You won't be able to "cut" everywhere, like a web page. In those cases, I select all, copy, go to "notes.app" or if it's short, the URL bar. From there I cut out the bit I needed from "notes.app" and usually go right to the app I want to paste to without issue. Though sometimes I do have to take a middle step and paste to the URL bar.
SOmething aboit bout the irk bar that allows copy to work a bit more reliably though still not 100% perfect.
HOpe this helps some of you until Apple fixes this, which I have a feeling is going to take a long time as is usually the case with what I personally consider huge mission critical bugs but Apple seems to de-prioritize.
Didn't it take until around version 3 of iOS to even get copy and paste? Granted, I'm glad they took the time as it works remarkably well when it works. Compared to Android, copy and paste is this beautiful, fluid, logical, self teaching function. On an Android based system, I have to think really hard about how to activate copy, and selecting columns and ranges off of www pages, compared to iOS it is a nightmare. Yet Android users seem to not be bothered. Probably because even if the implementation is crap, at least they *can* copy and paste. 😟
