So the general idea behind the deck is that the Asutra cards synergize rather well with Fydraulis Harmonia, what with the Synchros; Fydraulis has some natural synergy with the Dogmatika cards as it also sends Extra Deck monsters and the Dogmatika can provide a Normal Summon to give the Asutra a Set card to go off among so much.
So in more depth:
Asutra Yoa and Mikumari are your main Asuta monsters to see. Yoa is very important as it sets up your Level 8 Synchro as well as the other Asutras by setting a Trap from deck with Mukmari being another way to get to Yoa while being a better Synchro Material. If you need to search with the Field Spell, search Mikumari (since you'll need a second Set card to summon her) then Yoa.
If you feel the Synchro isn't necessary, that you're gonna get Droll'd or that you're playing under Nibiru: Go for Akasuna in most situation, then Kuzuha. Akasuna is more useful in most case as a Book of Eclipse on a 3000 ATK body and the ability to set up for the Level 9 Synchro for a mass disruption is great. Kuzuha is more of an OTK/kill push. You need a good number of Set cards to even get one pop (which given F&V is so prevelant, can be an issue), though the GY Set meshes well with Akasuna.
I run two of each Synchro since I wanna make sure I have extra access to them. You can run 1 of both to make some more room in the Extra Deck, which can be nice for certain packages I'll mention at the end.
The Field Spell is a 3 of to get to the Asutra side of the Deck. Believe it or not, this side is the one with the real firepower. Book of Eclipse, non-targeting/non-destruction send and a mass non-targeting banish is a lot stronger than a restricted targeting banish with some Extra deck help. It also has great synergy with F&V+Albion, as Albion's End Phase set can trigger the Field's bounce effect.
As for the Traps: I run two for each because they're all pretty necessary for the deck to function and they all have their niche cases. Roar is the best as a simple monster pop, Domain is a good insulator against board breakers and Poison can bring back a Asutra like Akasuna or even Yoa for another interruption. You'll be mostly using these to Synchro Summon, though.
For the Dogmatika cards: Three Eccelsia is a must. The card is the only normal summon in the whole Deck and it greatly helps the Asutra side of things. Cool thing is that since Eccelsia's Extra Deck lock is only for your turn, it's a non-issue for the Asutra cards.
Three Fleur Thunderbolt for a Turn 0 option, one that doesn't really affect the Deck since Punishment's lock being two turns only lasts for the opponent's turn 1 and your turn 1, where you don't do Extra Deck summons. And even if you can't use Punishment, it can still be used later for an Asutra summon. Also a free 2500 ATK body helps push damage.
1 Lawbringer for a combination of an extra ED interruption and recycling for F&V/Punishment. It's also a Turn 0 interrupt by that logic but not as flexible as Thunderbolt.
3 Nadir Servant to help get to Eccelsia with the hand summons being an option if you already have her, with the ED send either fetching F&V. fetching one of the hand summons/Punishment, setting up Black Dragon Eccelsia or even a generic ED breaker like Golden Cloud Beast or Packmister. Again, it's ED lock means nothing for this deck.
3 F&V (AKA The Falled And The Virtuous). Just in case you don't know why this card's so good: It's a pop for any face-up card on the field that can also be Quick-Play Monster Reborn if you have an Eccelsia on field or Grave. This includes the Synchro. It's also very searchable, especially in this deck with Dogmatika Eccelsia, and can be searched out by Albion after being sent.
3 Punishment. Like I said before, this card is basically the prototype for F&V. While true that it's a Trap that needs to be set to work and it's ED lock can screw you over if you don't sequence it well: It's still a searchable monster pop that can net you extra advantage, which becomes even better through Thunderbolt giving you more Turn 0 options. And again: it gives the Asutra cards another shot at being summoned.
For non-engine: Three Imperm because out of the common Trap Card hand traps, it's the only one that doesn't screw with the Deck. And two Ash Blossom, because it still gums up hands. A third could be useful with better ratios.
For the Extra, aside from the Asutras I covered:
2 Albion, 1 Titanklad, 1 Devours The Dogma and 1 Black Dragon Eccelsia as the F&V/Dogmatika package. Titanklad is here as another way to search/summon Eccelsia or the hand summons for extra grind. Same with Devours, except it can add F&V in exchange for no possible Eccelsia summon. Albion is obvious, with the extra synergy with the Field Spell. And Black Dragon Eccelsia unlocks F&V's second effect and can recover resources while also poking holes in boards.
For Punishment/Fydralius: Golden Cloud Beast, Engimaster Packbit, Psy-Framelord Omega and Despian Luluwalilth. The first two are differing forms of disruption, Omega recycles itself and another card for a minor but infinite recursion and Lulu is another way to access Eccelsia or Thunderbolt.
The two odd ducks left are Dracoberserker and Nacy Dragon Mech as side grades to the Asutra synchros. Need a banish in response to a monster effect instead of a GY send? Go Dracoberserker. Need negation with Eccelsia, Golden Cloud and/or Fyrdralius in grave? Navy Dragon Mech.
The side doesn't contain any actual side deck cards (kind of) but instead has options for the deck:
-OG Fleur for more damage and more monster hate. Doesn't help Turn 0 unless you have her other self or Lawbringer. Kind of underwhleming.
-Stardust Victim Sanctuary for another part of the Fydralius/Punishment package. You could do the OG for protection against breakers, obviously, but I wanted to highlight Stardust Warrior as a Summon negate. You could also do Stardust Spark if you wanted, though I'd say it's the weakest of the three.
-N'Tss. Classic Punishment target. You can swap out one of the other odd ducks for this, though it's a bit more clunky.
-Ultimaya. This is an edge case but Fydralius is, again, a Tuner. If you have one of the Level 7 Asutras on field with it, you can pivot into Ultimaya. And since you WANT to Set cards, Ultimaya's effect can fetch any Level 7 or 8 Dragon Synchro. Crystal Wing is just the most blatant.
-Dogmatika Maximus. The Extra Deck rip can really screw over certain decks...but F&V is almost omni-present so not the best idea.
-Encounter as an extra Trap set off Thunderbolt. I hope Konami prints another generally good Dogmatika trap.
-Aggregator for a negate off of Punishment. This also represents the other more generic Punishment targets.
-Albaz for using Titanklad or Devours for a Super Poly.
-Hope Harbinger and Dingirsu. This deck runs a lot of 8s that you could pivot into one of these two, who can insulate you against F&V and breakers.
-Fuwalos and Nibiru for other handtrap options.
I am not a good deckbuilder, that much is obvious. You probably only need 1 of each Asutra trap, you could probably cut a Field Spell and Nadir, cut Lawbringer and Dracoberseker/Navy for better options. This deck is also not the best Abyss-related mix with Asutra. The White-Albaz package gives you better access to 8s, better Albaz breaking and is smaller for more non-engine/First Penguin which does a lot of similar stuff for this deck. But I found a surprising amount of synergy here. I like decks that go 1 for 1 with a good amount of flexibility. And I think anyone else who likes this gameplay will like this deck.
Also kind of a crime more people aren't trying anything Asutra.
(P.S. Sorry if this sounds incomprehensible or anything. I am typing this at like 2 AM and I'm not a competitive player so...my insight might be garbage.)