I'll be publishing a Firefox extension as a temporary fix, will post it here. (I don't use Chrome.)

I think tampermonkey code is a better solution?

I've made the extension, but I haven't been able to test it (hence I'd rather not release it). I use Claude daily, but I haven't bumped into the situation yet where the generated output would disappear.

Good news, I caught it today, I'll be able to iterate and at some point I'll publish my extension at Mozilla.