If you open the bound cages in the Bound Sentinel fight in Boss Rush, the cages remain open in future waves.
Unfortunately, the cages do not close when the portal closes and is re-opened, so if you open them once, they are open forever. This can add extra difficulty to the fight which players who have never opened the cages will not face.
I could see letting them remain open for the current boss rush session, but I just ran my first boss rush with this character for the first time in over a month, got to the first sentinel arena, and it was completely packed down there with the whole lot of them before I even dropped down from the tunnel. I then quit out of the boss rush realm, closed the portal, played around with crafting for 20 minutes and opened it with a fresh card, and again the very first sentinel arena was immediately filled with all of them.
So this unlocked state for all enemies persists through portal closure, realm reset and a month's worth of total inactivity.
This arena should reset the same as the others, especially since there is nothing ingame to indicate any reason not to go upstairs, or to suggest that those traps upstairs are any different than the (largely inconsequential) other traps elsewhere in the game. The only way for a new player to know in advance not to do this would be to somehow go to the discord and ask "what can I do to make the bound sentinel fight exponentially harder for the rest of eternity?" before opening their first boss rush.