WHM uses a few attacking and healing actions (ones we're used to seeing) to build a new gauge. They apply a barrier using Stoneskin, a returning action that now costs a Lily (thereby preparing Misery in the process).
At 50 gauge, they use a big healing move that modifies the gauge to have 3 'charges'. The clip ends with them firing off Misery, Quake, Tornado and Flood.
While multiple targets are being attacked (eg there's a tank on either side with a mob attacking them), SCH uses a bunch of tactical stuff, combining healing actions as we've come to expect (eg Recitation > Excogitation, Adloquium > Deployment) to manage both tanks' HP bars. While the SCH is putting up their DOTs (3 of them in total, Biolysis, Miasmalysis, Shadowflare) on one of the mobs, more enemies join the fray on that side. The SCH hits Chain Stratagem, and Baneful Impaction, not only applying the AOE DOT to the group, but spreading the original DOTs (And Chain) to the whole pack of enemies. They then use a new action, Synchronization Tactics (replacing Dissipation), to empower the Faerie, putting Fey Union on the tank handling one enemy, while the SCH and Faerie work together via Sync to focus heal the one with more enemies attacking.
AST throws up Divination and Oracle, but then follows up with playing a total of three different arcana (2 Major, one Minor) on the party. Additionally, in the midst of playing the cards, they burn up one Minor Arcana to the Royal Road, and empower the second Major Arcana they play. As the clip continues, the gauge shows that the cards are not just 'once per minute', but available far more often (eg Minor Arcana being every 15s), and are far more easy to manipulate via Redraw and Royal Road, making setting up for burst windows far more accessible. It also reveals that, rather than using just two cards from the Minor Arcana (there's 54 in total), we can use all 6 suits (Cups, Irons, Crowns, Rings, Staves and Knives), and that the gauge indicates that each Arcana has a 'favoured role' (EG The Bole is best used on a Tank, and the game indicates as such on the gauge)
SGE fires off two new attacks, one a line AOE and one a Cone AOE. They relentlessly attack the target, weaving in actions that augment Kardia (adding the stacks to the Job Gauge), and generate a purple gauge as the stacks are consumed via attacking. This purple gauge is later revealed to grant a pseudo-Enshroud, or Hypercharge from MCH, allowing the SGE to attack even faster (and thereby heal faster via Kardia). As the clip plays out, they use a 'Eukrasian Phlegma', Psyche, a regular Phlegma, augment themselves with the Purple Gauge, then rapid fire the Line, Cone, Line, Cone, and finally finish off with Pneuma, now reworked to be a strong finishing attack.