When I go to type a reply or make a post on mobile, I can’t access my clipboard. I can still copy/paste the most recent item in my clipboard history, but I can’t access the clipboard itself.
That is an arbitrary limitation of whatever keyboard app you are using, or perhaps an artifact of your keyboard’s interaction with your browser. It has absolutely nothing to do with the VEX Forum website.
Furthermore, the “clipboard” as you describe it is not a feature of Android. Rather, it is simply the result of your keyboard app saving a log of everything you copy to the Android clipboard (which only stores one item).
For what it’s worth, Gboard seems to allow its multi-item “clipboard” to be invoked in while replying in the VEX Forum PWA, though I do not actually use the feature since I would rather not have my keyboard app tracking any text I ever copy.