I'm going to rant. Brace yourselves.
There is no way to search for Mycroft-centric genfic on AO3. None. You can search for fics with his character tag and the "gen" category tag, but this is a nearly useless filter. Here. Check it out.
Some observations on the results:
Mycroft isn't necessarily the main character in a listed story. He gets tagged as present even when he's an incidental character.
Relationshippy fic is tagged as gen. The presence of pairing tags with slashes between the names (Sherlock/John) is not at odds with the "gen" tag as far as the archive is concerned.
Crossovers are included with the default search; there's no way to get rid of them.
The "Case Fic" tag looks very useful. I'll start searching for that.
Why is a "mystery work" that I can't even click on to read shown in the search results? Talk about useless.
Phrase-length free-form tagging is lovely as an indicator of which stories to not bother clicking on at all, but neither a help nor a hindrance in the search. I wouldn't bother suppressing it.
In the end, I'm left doing a FF.net-style browse down the list, reading summaries to figure out which stories I want to read. However, there's far more noise in the list because FF.net allows at most two characters to be attached to the fic. So if somebody marks a story as featuring Mycroft, it probably does.
In fact, here's the FF.net Mycroft listing. Dude, why the hell was I bothering with wading through the AO3? That list is obviously far more relevant to my interests, right there on the first page. There's a significant content overlap between the two archives but FF.net makes it easier for me to find what I want. Yeah, it doesn't let me filter out gen vs shippy fic, but as we've seen, AO3 doesn't really either. It merely makes me hope that I can.
And ff.net is faster.
In the end, I think relying on a trustworthy rec list is the best option. I was willing to read every single Giles story in existence hunting for good ones, so I was writing some of those rec lists. I am not that much into this fandom. I read a story last night and was out the very instant I saw the writer use "taught" when they meant "taut". No patience.
I'm writing post-Cruciamentum Giles/Buffy right now, by the way. Yes, that demon-transformation soul-bonding wingfic is post-Helpless. Have been challenged to include knotting in it, but no, it's not that sort of story.