Issue: The DB's weaknesses make it feel overly punishing to use and aren't interesting to play against.
It ends up being overly polarizing because it needs to have such bad range and a crippling passive knockback penalty to compensate its high no-hp-cost mobility. The passive knockback penalty in particular is a poor design because it feels terrible to use, but doesn't offer the opponent tangible and consistent ways to take advantage of it.
Suggestion: Remove the passive knockback vulnerability and replace it with something else.
I'll list some ideas but I don't know if any of them are perfect fits:
1: Reduced reload speed. This would help reduce the overall mobility boost, but wouldn't be something the opponent could actually feel in an interaction.
2: User has some kind of extra vulnerability while DB jumping. This could be something like a mark for death or even just having the knockback vulnerability be only during DB jumps at a higher magnitude. This could give players a chance to punish the pyro for using it too aggressively or often without punishing the pyro just for having it in their loadout.
3: Holding the mouse down before shooting the gun causes it to gain knockback over a charge period (similar to the loose cannon's fuse). This would make it worse at overall mobility and worse at jumping while in fights in exchange for the option to use it midair without inflicting self knockback. It could also have an accompanying stat like having its spread increase or decrease with the charge level to give it more flexibility.