I can confirm this is a bug. It may silently happen on the last turn even if you use autosave to repeat it (and only then you may sometimes see it if you wait for a while), where Drain the Swamp will activate despite the lack of prompt when results are supposed to be processed.

But this is definitely a bug. The best counterplay to drain the swamp is to place enough cards or operatives cards to bait it out - but even then there is no guarantee the AI will use it! Or to have a gameplan that can't be disrupted by it at all. More often than not the AI may give up its hand or advantage playing it too. It's tricky!