So I don't know for you guys, but I am finally up to uninstalling Opera. I was struggling the last few versions (since 58), now I'm going to get rid of this piece of user-unfriendly crap. Have a nice struggle with the sidebar.
It works in Opera for something simple like http://jkorpela.fi/forms/form1.html. Clicking back after submitting will still show your form changes. But, if you reload the page, Opera will clear them. For Firefox, it won't even clear the form changes when you reload the page unless you do shift+ F5 or something like that.
Here's some history on how this feature came about: https://bugzilla.mozilla.org/show_bug.cgi?id=46845.
As for why the page you're messing with doesn't do it in Opera, it might have something to do with the search page you're returning to not having been cached. Maybe check the headers the server sends? Or, it might have something to do with POST vs. GET. Either way, Opera doesn't retain form changes the same as Firefox. Firefox is more advanced.
I don't know if there's a workaround, but if you can find one for Chrome/Chromium, i might work in Opera too. Perhaps there's some extension that can do it.
Made a thread asking for this around 9 hours ago. Didn't get much of an *useful reply... https://forums.opera.com/topic/34840/not-accepting-webm-or-mp4-for-custom-animated-wallpaper-anymore
.webp files work, but no idea how to make them work to look as good as a .webm file.
Not a deal-breaker for me, I'll just get another animated one from the addons page, but I really liked my previous wallpaper.