It's a little 'boomy' or microphonic, the tone is not bad but can be improved.
Which? I kind of think of those two things as different symptoms. Microphonic means the pickups hear things other than the strings... like you can talk near the pickups and hear your voice in the amp's output. I mean, you can with lots of pickups, but some are far worse than others in that way. Microphonic also can mean whistling feedback when turned up, or possibly howling feedback down low.
Booming though - that's interesting. I wonder if that's a setup thing? or possibly an amp thing? What other basses have you tried playing through your current amp setup in it's location (in your home)? Like, if you haven't tried other basses in your setup, it could be the amp or it's settings or the location in the room, not the bass.
Also, the P pickup might be too close to the strings - I often put bridge pickups as close as possible and neck pickups further down, but balance between them is super important.
With well matched pickups (both electrically speaking and output level and tone-wise), you should be able to have them get similar output levels soloed, then blend really well together. But some pickups aren't well matched and that never works right.
One would THINK that those stock pickups are well matched, since the company that made the bass isn't stupid.
But setup could still affect things badly.
I owned an affinity jazz bass 5 string - it sounded like crap when I got it (For like $20 from a kid). I set it up like crazy (shimmed neck cuz couldn't get proper setup angles otherwise), adjusted bridge saddles, intonation, filed nut slots some, filed a couple of high frets in the upper octave (where they typically aren't well levelled on cheaper basses), and then put on a nice set of strings (I think I probably used elixers... that was back in one of my elixer periods). I also setup pickup heights - listening to only neck pickup, raise it as much as possible until it starts to sound bad when playing up the neck, then lower it a spec until it sounds great no matter where you play it, and so it isn't too high to mechanically get in the way when slapping or playing hard with fingers. Then I transitioned back and forth with only neck pickup then only bridge pickup, adjusting bridge higher and higher until it's level matches or very slightly exceeded that of the neck pickup (personal taste), and then put them both on full , made sure it sounded awesome, and voila. It because an excellent instrument that i'd be perfectly happy recording with or gigging with. I sold it for a profit (made like a hundred bucks! LoL).
I know the 4 and 5 string ones have different hardware (tuners, pickups), but I'm sure the 4 can be setup to sound great also.