No, this door is supposed to remain locked, there's no hidden ending behind it so I think you found them all, well done!
Idea for consideration, and light spoilers for anyone not related to the convo:
It feels a little off that after you talk with Tray after activating the final timer that nothing happens. Maybe instead make it not a live timer, and maybe Tray gives a clue on an action to perform to get another key for 1-C, which has some more story and gives Emilia
the idea to take the thing out of the tank, go to the pier (which otherwise feels kinda empty even with the purifier), and dump it into the ocean, which results in a final true best ending.