Love the game! I just have a few suggestions:
First of all, I found a pretty easily fixable issue about movement. It seems like the player's movement vectors aren't being normalized, resulting in the player moving faster when running diagonally and even faster than that when jumping at the same time. I was able to abuse this to just skip through the Pit of Pain level without firing a single shot or taking a single hit from an enemy.
On the topic of the Pit of Pain level though, I found it to be rather unbalanced. Taking the left path from the start along the top (as I did) left me starved for ammo, and having to melee by the time I reached the bottom. Even when I used my shots as efficiently as possible (that is, only using the minimum number of shots per enemy) I still found myself critically low on ammo by that time. I think this could be fixed by making the level more linear, making it so the player can't take the left path and has to go to the right. While this might take away from the openness of it a little, I think it would improve gameplay as there are plenty of branches to the pit along the path to the right.
There are also some changes to the gameplay that I would like to suggest:
First, I would make it so that when the player shoots one enemy, the ones around it are alerted as well. It's easy to play the game as a stealth shooter rather than a run-and-gun DOOM or Quake style game, picking enemies off one-by-one.
Something else which I feel kind of slowed things down a bit was having to switch to a separate melee weapon. The sword felt a bit awkward as the only melee option, since it takes time to switch to it that could be spent shooting. I think that it would feel more natural if there was also something like a punch that you're able to perform while holding guns. It could deal low damage and be more focused on knockback (similar to Left 4 Dead), so that way there's something to fall back on if the player gets surrounded by enemies. Also, punching a demon to the ground before blowing its brains out with a shotgun is really satisfying!
I think the rage mechanic is a bit underutilized as well. I think that a system like that should feel as good as possible to play. Instead of just speeding the player's movement up, a solution could be to also increase the player's rate of fire. It could also lead to the player bringing out a chainsaw or something while giving a speed boost to annihilate enemies that stand in their way (but still be vulnerable to damage, especially from ranged weapons). I think that adding either of these would dramatically improve the rage mechanic.
Finally, I found the explosions to be a bit lackluster. The explosion radius is rather small, making it not as effective for large crowds as it could be. A solution to this (without making explosives overpowered) could be to have a "core" to the explosion as well as an outer boundary to it, kind of like a shockwave. The core could deal full damage, and the explosion could deal less damage the farther away from the core it is until it finally drops to zero at the outer boundary. This would make it so that shooting a pipe bomb into a crowd feels more effective, even if most of them don't drop dead on the spot.
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Regardless of the suggestions though, I had a great time playing this game, and can't wait to see more!