To me, them rising to prominence in the Adders by the time we see them next would be the most "win" I can imagine for them.
Imagine we see Clan Star Adder again in the universe again, and it's Khan Michael Faraday and saKhan Abigail Breen in charge. Not only have the Adders put those bloodnames to work, they've risen to some prominence in their new Clan. That would be.... amusing.
As for challenges and contests, they do have other Clans to spare against. It's just not as many as before. But they never were engaging with ALL the other Clans all of the time. Pre-Wars of Reaving each Clan typically had its 1-3 Clans that it was feuding with that it fought a lot and the others not as much and some Clans they didn't engage with hardly at all. But as part of the Clan way, you even Trial against your political allies sometimes as a way to settle disputes and provide that challenge for your warriors that you spoke of. So, I'm less concerned about this.
The Adders were also the Clan that had an OpFor Galaxy, to spare against internally. So yes, they might invent ways to spare against each other internally. But they can do it in ways that don't incur as much death and equipment destruction, but still provide some version of honor/glory/bragging rights. Think about Clan equivalents to the Martial Olympiad by various unit size scales. As long as that society agrees there's honor and prestige in it (e.g. doing well there can make you attractive as a contender for a Bloodname), it should sate some of the warriors' need for that kind of thing.
But doing it along the lines of these old dead Clans isn't smart. Better to put the warriors together by units, by Clusters, Galaxies, and build up a strong cohesion with their fellow warriors (not segregated by bloodname origin).
At this point the Clans gotta be looking at the Fire Mandrill Kindraa system and see is as purely a failure. They survived, but they never really thrived and then they died. It's clear by the opinions the other Clans expressed of them in FM: CC and FM: WC that the other Clans (except perhaps the Blood Spirits, but they are gone too) never really had a high opinion of the Mandrills. Not something you draw inspiration from.
As a faction I actually find the Mandrills interesting, I particularly loved the detail the Mandrills' entry in FM: CC gave to some of the Kindraa bloodnames. Telling us what they were good at, showing more of the Bloodname House politics that I find interesting. But the Kindraa system provided more downsides than upsides. I really think the only reason the Mandrills survived for so long is because the nature of Clan Trial warfare in the Homeworlds limited the scope of potential damage, and confined a lot of Trials to small scale affairs. That environment, the Mandrills could manage to hold their own in. They just had to make sure no Clan ever went total war on them, in a manner akin to the Adders versus the Blood Spirits even pre-WoR. Or in a manner akin to the Wolves vs Jade Falcons in the Refusal War. They were never going to survive that kind of full court press, and amazingly they avoided that scenario, until the Wars of Reaving happened.
Personally I'd argue that the Mandrills as a Clan died at Arcadia. Payne-Beyl-Grant showed up and declared Reaving Trials for Snuka and Vong. They got obliterated in that fight.
The very next move we read about, the Goliath Scorpions, Steel Vipers, Coyotes and others are moving against Mick-Kline-Kreese-Sainze to reave them. The Mandrills weren't a tainted Clan. So it wasn't about taint. I think it was because at that point the Mandrills had 3 Kindraa left, probably just three Galaxies, and those galaxies were fragmented Kindraa style. The other Clans decided that the Mandrills were now weak, too weak to be a Clan, and needed to be removed from the board. Yes two Kindraa survived past that point, but even without the Wars of Reaving they would have been easy targets for absorption, and as the WoR did happen, they largely fell to starvation and plague.
The Homeworld Clans decided that the Mandrills needed to go, but the Mandrill eugenics program was full of generations of genetic legacies of elite warriors with an excellent codex (and no Inner Sphere taint). Some genetic diamonds to be dug up in there.