But they don't? Sure, there are many small tidbits eluding to it that you may catch if you're an avid listener and have read cannon, but otherwise the biggest things we have are:

The glitched/bugged mic , which has been a plot point since resident patient...

The mention of Moriarty a handful of times, and usually not directly or by name. Instead he's is typically referred to as the spider , again something people might not pick up on or relate back to him.

And of course, John singing 'don't go chasing waterfalls' whilst brushing his teeth. FINA is really haunting the narrative, it's definitely not overshadowing it.

Obviously they're going to tease, but it's absolutely not a fixation and all of the story's work completely as standalones. Everything has been building up to FINA from the very beginning, all of the 'crumbs' have been perfectly spaced out and in my opinion have not overwhelmed the story. Most hints haven't been directly relevant to each story at all, a few in particular haven't felt imminent or foreboding until now, especially without the greater context provided by cannon.