Zethi plays like an aggressive/tempo control deck, trying to lock out the opponent as fast as possible. Its game plan is essentially to accelerate into getting Zethi online and acting as the deck's primary card draw engine and repeatable threat removal, providing inevitability in attritioning the opponent. Since Zethi is so critical, it has a lot of protection most commonly in the form of counterspells and blink/flicker effects. Since Zethi provides a steady stream of cards, this deck can utilize high tempo low value cards to get ahead quickly without running out of steam later on. This deck technically wins through Commander damage, but in practice it should have clearly locked out its opponents far sooner and probably should result in concessions. Since so much of the deck is instants, it plays like a draw-go control deck. In multiplayer, this deck relies a little bit on politics and threat of retaliation to stay alive. The general early gameplan for Zethi is to get at least one card draw spell for value and at least one blink/disruption spell for sustain (with blink ideally translating into disruption/more value later on). If not pressured, it can hold off on casting Zethi to get more, but this may be enough to close out the game and thus Zethi may only need to be cast once and this is the minimum set of spells to aim for.
This deck wants to float mana to be reactive. In order to not fall behind on tempo as a result, it wants spells that are:
Cheap/Free. It wants to need to float as little mana as possible.
With Zethi serving as a card draw engine, ideally cards bias towards cheaper for less value. Riders such as "draw a card" are actually often detrimental since they usually mean higher cost, though some exceptions may be okay, such as otherwise situational cards that also have some value in being recast by Zethi.
For reactive spells, 3 mana cost seems to be average/acceptable, 4 needs to be justified, and 5 seems to be untenable. Spells mainly intended to be recast (not mutually exclusive with reactive spells) also want to be cheap to allow for more floated mana, but can be a little more expensive if justifiably strong.
Flexible. It wants to be able to spend that mana even if there ends up being nothing to react to.
With protection spells, these ideally want to be flexible in that they can be cast meaningfully even if no protection ends up being needed. This is even more true when there are multiple protection options available and you no longer need them all. Ideally they can serve some other purpose, and even more ideally not in the form of value but in the form of tempo. This flexibility ideally also means that they can be played early (and thus be in the graveyard for Zethi to kick) and recast meaningfully.
Hard counterspells naturally fit well here. 2 mana hard counters have been especially great for both being flexible and cheap.
Blink/flicker fits this as well. It's often good enough for protection but also flexible in that it can be used on ETB creatures for other tempo/value effects. Even without ETB targets, they can be recast as combat protection since Zethi needs to attack. This theme also takes off some pressure from Zethi being the only thing that makes the deck work and thus the sole target for removal.
Scaling. Effects that in some loose sense "scale" into the late game tend to be better. This includes counterspells (counter bigger spells), blink/flicker (improves as better/more ETB effect creatures are played), removal/bounce (targets bigger creatures), card draw (draw late-game oriented cards). These allow for being played early (and thus being in the graveyard to be kicked) but still being relevant when recast later, which allows Zethi to stay online/relevant longer without needing to be recast for more kicks.
Some effects that don't work as well:
Stall that isn't tempo-equalizing (tap vs. bounce) is unsustainable. Similarly, non-tempo-equalizing stalling creatures also don't work as well.
Self bounce does not seem to be necessary. Zethi may only need to come out once to close out a game. Having a slight focus on mana ramp also helps enable Zethi to be threatening enough on the first play that the opponent will want to remove her (and thus letting you recast Zethi if desired).
Mana base prioritizes fast mana. This deck is very mana hungry and tempo focused so it does not want to fall behind on too many tapped lands and wants to ramp as fast as possible in these colors. Like with other cards, it does not need extra value from its lands since Zethi provides the value, and thus prefers tempo for lands (ETB untapped). It has a decent number of cards that interact with basic land / land types and thus has a fairly high concentration of basic lands. Some cycling lands can be okay since Zethi can whiff on assembling its engine. Cheap draw that digs also can help with getting lands. Blink targets for ramp can also help accelerate mana.
Because of the way it plays and its win condition, this deck can feel unfun to play against for some and thus may not be appropriate for all situations. For similar reasons though, it can also be a little more competitive with its power level. Still not aiming for it to be as competitive as possible, but it can have thematic tutors, pure card draw, and employs a lockout gameplan. It can also aim for slightly more consistency than the other more casual Commander decks.