I believe this is the secret level: https://www.commander-keen.com/level-maps-1.php
We called it the Teddy Bear Maze, for its higher occurrence of teddy bears than other levels. Though looking at the layout now, I don't think it quite deserves the 'maze' designation as much as the Pepsi Maze does. But all those teddy bears...you could rack up a few extra lives if you managed to snag them all.
Looking at the levels, this one raises my curiosity: https://www.commander-keen.com/levelmaps/1/015.gif Note that there is a yellow keycard, but not a yellow door. I'm thinking either the level was never quite completed, or whoever took the screenshots to make these images took one after opening the yellow door. Reflecting on it now, I think perhaps the latter was the case, though I don't remember where the yellow door was. Either by one of the robots, or right before the drop out of the colored area.
Not sure if a mistake or red herring; probably the former but in a more tortuous level layout it would be kind of funny/cruel to make people work to get the green key to get the yellow key to get nowhere extra at all...
Thanks to khedoros1 for linking to the wiki, which has lots of good stuff on (and also lets you look at the level maps while the originally linked site is down): https://news.ycombinator.com/item?id=14656926
My favourite bit was the dark, fiery secret tunnel underneath one of the larger levels (http://www.commander-keen.com/levelmaps/1/013.gif), which teleports you to the city on the right-hand side of the world map at the bottom of the level maps page, not really visible from the map screen when going between the main cities... but I no longer remember which of these maps is that city, alas
(or maybe not alas: I hope I've put some more currently useful information in that part of my brain instead. Thanks for the nostalgia!)