While I usually use PbtA style initiative in my games (simply following the narrative and making sure everyone has equal spotlight time), there are some other initiative systems that are enjoy.
Super fast and simple - Savage Worlds: Each round you deal a card to each player and each mook group. Then you count down from Ace to two. There are mechanical ways of drawing more cards and keeping the higher. In my games player and the GM kept their cards secret, so it is more exciting to see when someone acts and how the combat will proceed. There were also ways for players to peek at GMs cards.
Super Thematic - Doctor Who RPG from Cubicle7: Initiative works depending on what you will do. It goes Talk -> Act -> Fight. So if you try to talk someone down you go before they will have a chance to attack you. If you try to do something clever, like close the mechanical door between you and the attackers, you get to try that before they attack, but they can still try to talk you out of it. It all fits very well with the source material.
Fast & Thematic - Marvel Heroic RPG (this might also be used in other Cortex+ games, not sure): one player has initiative, then after their turn they pass it to another player of their choice who hasn’t acted yet, or to an enemy. It makes for fast gameplay & mimics the style of comic panels (Wolverine punches a dude, two more baddies rush in through the door only to be blasted by cyclops).
All of those can easily be ported to the game of your choosing…
@Lu.Quade - for those of us who are not familiar with Troika, can you tell us how the initiative works in the game and what makes it so chaotic and unpredictable?