During Phase 1, the two Achievement systems will live side-by-side as we decide what the best way forward is for our users with a great achievement experience.
It isn't clear if new wikis will be able to enable Achievements but it seems that they have the intention of porting it. Or at least, finding some way to preserve the achievements for wikis that already use them.
Fandom has recently released a new platform (called United Community Platform or UCP for short) that they are using for new wikis. This new platform is missing a lot of features available on the older platform. They are working on adding some of the older features to UCP (referred to as porting). However, they have not released a list of features that will be ported. So right now, we can only guess if Achievements will be available on UCP wikis.
Fandyllic is saying that Achievements is an old abandoned extension. This is true. That is why he is saying he doesn't think it is likely to be ported.
On the other hand, MisterWoodhouse (a Fandom staff member) told me that, during phase 1 rollout of UCP, Achievements will be kept. Phase 1 rollout includes converting all legacy-platform wikis to UCP. So if Achievements will be kept at least during this period, then that implies (but does not explicitly state) that there will be some adaptation of Achievements for UCP. However, MisterWoodhouse provided no details on what exactly this means. It is possible they just copy over the badges and points for display purposes but disable the feature itself; making it impossible to earn additional badges. It is also possible they may port it but only allow older wikis to use the extension.
The bottom line is we just don't know at this time.