smoky cedar
I had the exact same glitch down to the letter as @rose frigate, but decided to make another thread because I found WAY MORE glitches surrounding this boss that can break the game visually and mechanically.
The trigger to these glitches seems to be closing the game without beating Pepper after attempting him the first time. These issues began after I attempted Pepper 4-5 times, closed the game, and returned.
Bombs while stunned: While stunned, Pepper has been able to continue to throw bombs at me. (Edit: Turns out I did get video evidence lol, just noticed he does it when I stun him in the video below.)
Leaving the boss room: This glitch is always possible even without the presence of the other glitches as far as I can tell. Leaving the room before the fight is finished will always mess up the camera perspective if the fight is unfinished, leading to lighting issues and being able to see under the floor. This is fixed by resting. The boss bar remains after you leave the room, which cannot be fixed by resting.
Bombs through the floor: Pepper can sometimes throw bombs through the floor to the bottom of the map. I think this is actually possible without the presence of other glitches because it seems to keep happening in the same section of floor. Check for collision issues.
Idle Pepper: I have noticed some of these glitches happen depending on how many times you have walked into Pepper's room after launching the game. If you launch the game and walk in the first time, the floor will be broken as if you were already in stage 2, and Pepper will be idle and unmoving. HOWEVER, the spikes are just a visual bug and you can walk on the floor as if you were in stage 1 or pre-fight. By dodging through them, you can immediately access the room after the fight. Choosing whether or not to break Pepper and the henchman from their idle (which can be done by stunning them) has some effect on how they will act when you reenter without saving and enter after saving.
I have a video demonstration of all these bugs. My internet is a bit slow, so I'm going to let it send in the thread below after posting this.