Extradimensional Crisis looks primarily to be a "tools for other decks" kind of set, rather than spawning new archetypes all on its own. That said, there's more than enough to try in the early days of the set, so let's get cracking!
Buzzwole ex
This seems like the kind of aggressive deck that was almost built for us with the new set. As such, I'm eschewing the more defensive Leaf Cape and second Erika - at least for now - in order to accommodate 2 Repel, 2 Cyrus, the new UB-only Poké-tool Beastite, and a Red just in case we somehow can't close out KOs. Even a single point KO from, say, Kartana allows Buzzwole ex to hit the 150HP breakpoint with Red. Lusamine allows us to effectively toss our one-point Ultra Beasts into the meat grinder to trade up in order to fuel Buzzwole ex, and Celesteela as a one-of gives us the best retreat aid we can ask for.
Other options: Leaf Cape, a second Erika, Sabrina, Giovanni, Rocky Helmet, Ilima
Copium Pikachu ex
Yet again, we get a possible format-defining staple shadow-dropped in the set release; this time, the unassuming Item card Repel! Against any Basic-heavy deck (so, most of them), this is essentially a copy of Sabrina that doesn't cost us our Supporter use for the turn. It also seems like DeNa remembered that Pikachu ex is a card, as not only did we get the new Basic ex Tapu Koko ex, but also an intriguing Poké-tool seemingly tailor-made for our relatively scrawny Basics in Electrical Cord. Being able to reuse energy from a KO'd Tapu Koko ex or Pikachu ex in conjunction with our pivot potential from X Speed seems like the kind of boost this archetype sorely needed to keep up. The remaining support slots are fairly standard; it's possible that with Repel we may end up chopping the Sabrina for a second copy of Cyrus, but it's just as likely we'll need a way to shove something like Meowscarada out of the way to secure points. The main awkward part of building this deck is the point map, as we still need non-ex Pokémon to not get dumpstered by Oricorio. For now, the Safeguarded cheerleader is our remaining set of Basics, but this could easily change in the future.
Other options: Giant Cape, alternative one-point Basics, extra Repel/Sabrina/Cyrus
Bring Your Son To Work Day
There are almost certainly better competitive homes for Guzzlord ex and Silvally, but the idea of Gladion and Lusamine having some family bonding time was too wholesome for me to resist - shame that we can't include Lillie as well! The basic idea is to throw a Poison Barb on either Guzzlord ex or Silvally in order to get a benefit from Nihilego and its More Poison ability. Silvally is an oddly efficient attacker; 100 damage for 2 energy on a Stage 1 one-pointer is an incredible rate, and only requires us to play a Supporter. We were probably going to anyway every turn we could, so it's totally fine! Even the basic Type:Null is weirdly efficient, hitting an average of 30 damage every turn with Quick Blow while not sacrificing much in the way of bulk. Again, our point map is somewhat awkward, but ideally we can either disrupt enough with Grindcore or simply blast at our opponent with Brave Buddies before it becomes too much of an issue. Celesteela also feels somewhat awkward, as it can realistically only swap in itself, another Guzzlord ex, or Nihilego. Of all the slots in the deck that keep the theme intact, that one seems the most flexible.
Other options: Guzma, Red, Darkrai ex, Leaf, Ilima, Beastite
Metal Aggro
The predominant aggressive Basic in Space-Time Smackdown, Skarmory, got a couple of nifty additions. The first is a potentially nuclear finisher in Alolan Dugtrio ex; it has an EV of 90 damage for 2 energy, which is roughly on rate with Starmie ex, but can highroll and delete virtually any opposing Active if you hit the 12.5% chance to get 3 heads. The second is the shadow-dropped Claydol, which forbids all healing as long as it's in play. Erika, Irida, and even some Potion lines gave Skarmory decks fits before, and we have no ambitions of healing ourselves! Despite no longer being a pure 1-point deck, we can still get a reasonable point map by throwing two Skarmories at our opponent before swinging for the fences with Triplet Headbutt. We can even use Alolan Diglett (EC) as an alternative turn one attacker; the 50% chance to do 40 damage on turn one is nothing to scoff at! The main issue right now is finding spare deckslots to fit everything we want!
Other options: Guzma, Red, Giovanni, second copies of Repel or Cyrus
The Roman Candle
This deck has one goal, and one goal only: Blow massive holes in the opponent's Actives constantly! The Barry + Snorlax (TL) combination has already been used in concert with the similarly high-damage Giratina ex to present a barrage of 100+ damage hits. Lusamine can convert the energy from a KO'd Snorlax to power Blacephalon and enable it to Beat Punk and almost assuredly revenge-KO whatever is in play. Beastite and Red combine to add a potentially absurd 40 damage to Beat Punk; very little can withstand that much sheer firepower! This is a pivot-free zone; whatever we have in play is attacking until it gets KO'd! We have the luxury of Snorlax's natural bulk in order to consistently find our pieces. Repel and Sabrina let us counter our opponent's cowardly attempts to hide their premium targets behind tanks, especially our mortal enemy Druddigon.
Other options: Giovanni, Poison Barb, Ilima