D&D initiative tracking needs more than turn order

I keep using combat as a test for whether a tabletop tool is actually helping the GM or just narrating around the hard parts.

The scene in my head is the bell room above the Red Glass tannery. The party kicks the door open after chasing Varric, the knife-priest, up three flights of wet stairs. There are four things that matter before anyone rolls damage: Varric is one round away from cutting the rope on the alarm bell, the brass brazier is already spilling coals across the floorboards, the fighter is standing between two vats of blue dye, and the apprentice the party came to rescue is gagged under the west window.

A plain initiative list can handle whose turn comes next.

It cannot, by itself, carry why the turn matters.

That is the part of D&D initiative tracking I care about right now. The useful question is not only "who acts first?" It is "what pressure is alive when this turn starts?"

If Varric goes before the rogue, the bell rope matters. If the wizard acts before the coals spread, a cold spell can buy space. If the fighter spends the turn crossing the room, the apprentice is still under the window when the hired swords come in from the stairs. If nobody deals with the brazier, the map is different next round.

For Trismeria, the public direction is an AI game master for authored fantasy tabletop campaigns. So I do not want combat support to become hidden prose with a turn order buried somewhere in the answer. The dice, character sheets, map position, and scene pressures need to stay visible enough that the GM can make a fair call and the players can make a real plan.

A combat turn probably needs a small packet of state, not a novel:

who is acting now

what they are trying to do

what visible threat will change before their next turn

what object, NPC, or map feature can still be used

what consequence is already in motion

That is not about making every fight tactical. Some fights should be quick and messy. But when the room has a bell rope, burning coals, a hostage, and a villain trying to leave, initiative should keep those things in the conversation.

My current test is: if I hide the initiative tracker, does the fight lose only order, or does it also lose the situation?

If it loses the situation, the tracker is doing too little.

For GMs: what do you wish your initiative notes showed besides names and numbers?