Though it’s ultimately academic as Tyson exists in a world with (limited) magical influence and duplicate Moriartys, within the timeline of BBC Sherlock canon, Tyson technically becomes an AU after Series 2.
That said, elements of Series 3 and Series 4 exist within Tyson’s world.
On the rooftop of St Bartholomew’s Hospital, Mischief earnt that nickname from his previous CCT. He faked his death with hyper-realistic blood packs and nanobots to ensure his vital signs were absent for any checks, should his clean-up team be delayed or his body intercepted before they could arrive.
Meanwhile, Sunshine was the one pulling the strings of the web to make sure Sherlock had to follow through with his half of the ‘deal’. Theoretically, Tyson was doing his part to make sure everything went to plan, but in truth, he was having his heart ripped out listening to John’s anguish.
Sherlock then went on to dismantle parts of the web, that is true. However, the Moriarty Mirrors viewed this more as a spring cleaning. They laid low for a while, protected what was essential, and allowed Holmes to tidy up anything that wasn’t clever enough to survive without linking back to them.
For now, with Sherlock’s return to London and notoriety, the Moriarty Mirrors are content to leave him alone to his own devices. If Sherlock is aware of their continued existences, he has also left them alone. Tyson doesn’t expect that peace to last indefinitely nor for the next round to end so bloodlessly.
Though John didn’t know that Sherlock lived before he returned, he knew that Moriarty was still around. Simply due to the fact that Tyson hadn’t fled London or committed suicide to escape The Colonel once more. Now that Sherlock is back, they’ve returned to pretend not to know who the other is talking about in relation to a maddening flatmate and an insufferable Irish boss.
Charles Augustus Magnussen is alive and occasionally has dealings with the Moriarty Mirrors, but the events of Series 3 around Sherlock have not happened yet in Tyson’s timeline; and aren’t ever likely to. The Moriarty Mirrors would not take kindly to him poking their consulting curiosity.
Though Mary Morstan exists, in Tyson’s main universe Mary is not currently married to John Watson; who moved back into 221B Baker Street a few months after Sherlock’s return to London. Tyson won’t even pretend to know the current dynamic of their on and off again relationship, but he can say with certainty that John doesn’t have a child with Mary.
However, John does have a beagle called Toby, previously called Gladstone at the shelter. He was adopted as a way to help John grieve after Sherlock ‘died’ and has since started working with Sherlock during his detective cases; having already received some training from Tyson during that year where Tyson could pretend that he and John weren’t still on opposite sides and could see his former brother in arms a little more frequently.
If she exists, Tyson has never heard of Eurus Holmes and the Moriarty Mirrors have never mentioned her either. It wouldn’t have been the first time they had kept secrets from him, especially concerned their obsession with Holmes, but to date, there is no reason for Tyson to know of Eurus.