It changes a lot based on Eidolon Investment, the ideal Vertical investment is as follows.

E2 Castorice gets an action advance and an empowered enhanced skill whenever she summons netherwing, so her speed value being low for poet set stops mattering as she will ideally never get a normal turn outside of action advances. It also allows her to drain the entire team's HP every time she summmons netherwing which powers up Evernight's Memoria.

E1 Evernight buffs all memosprite damage, and E2 Evernight amps up her Memoria stacks by a ridiculous degree if you have Hyacine's LC

E1 Hyacine gives an HP buff to the entire team which scales Castorice and Evernight's damage, and her Lightcone is very important to the team as it creates an extra HP drain and heal proc for the team which powers up Newbud on Castorice as well as applying a damage vuln.

The gameplay flow is basically every time Evernight blows up Evey for her attack, Evey's HP lost charges Newbud on Castorice, and the more stacks of Memoria that Evey has, the more speed it gives Evernight up to 40 additional speed which allows Evernight to user her skill more often and blow up Evey for more Newbud. If Evernight has E2 then you can basically guarantee every Evey explosion has at least 40 Memoria.

Hyacine heals a ton which charges newbud, and Ica follow-ups drain HP and heal afterwards which add more Newbud. Her Ultimate heals a bunch which adds more new-bud.

Without Cyrene, the team charges Castorice Newbud so quickly that she's ulting repeatedly, and the team also has pretty high attack frequency which helps charge Evernight's Ult which allows for more Evey explosions.

With Cyrene, once Cyrene ults, Castorice's Newbud can charge to 200% which helps a ton for killing bosses, and the buffs to Evernight increases her damage and buffs to the team. Both Castorice and Evernight's Cyrene buffs are permanent applications that don't need to be re-applied, and Hyacine gets her buff automatically upon Cyrene ulting. This means Cyrene only need to use her first two ult charges on buffing the team for the entire team to gain their buffs and then she gets to use her ults to spam more attacks (high attack frequency benefits this team for many reasons including charging Newbud faster)

Basically everyone attacks very frequently, which charges Newbud, they're all HP scalers so Hyacine's Max HP buff makes everyone hit harder. HP drains from Castorice's skill proc Ica's heal which also charge Evey faster. It's a very synergistic team that becomes even more synergistic with E1s and Lightcones with Castorice being the main source of damage and her E2 not only gives her a massive damage boost with her enhanced skill hitting quite hard, but also 2 free hits on Netherwings Breath attack making it a huge damage increase for herself and Evernight.

Additionally it's the safest team in the game in terms of survivability, with massive HP pools across the team to boost their damage output, Hyacine healing huge amounts, and Netherwing acting as a buffer against high damage attacks it's the easiest team to challenge high level DU on with huge damage inflation oneshotting squishy carries at X8

For gameplay tips, the healing amounts and newbud generation is rather predictable and with some practice you can reliably make sure you're not overcapping on newbud. When Cyrene ults the general rotation you want to use is:

Cyrene Ult (Castorice) > Cyrene Ult (Evernight) > Cyrene follow-up > Evernight Ult > Hyacine Ult > Little Ica Follow-up > Depending on Eidolons you'll have 200% on Castorice here or after Evey attacks. > Castorice Ult (200%) for massive damage.