As someone who is relatively new to bass I have learnt that “building the sound” is nearly ALL about how you play, yes there are some instruments that sound a bit different and some pedals and amps can change the sound but the magic in in your fingers (or pick!). After 3 years of learning I’m in a band and play a lot of different styles of music. I’ve found on most occasions changing the way I play makes the key difference( rather than changing an amp setting or buying a new pedal.
I play every way on my P-bass, from very soft, gentle and slow finger style (for ballads or when I play in my church) to absolutely beating the shit out of the strings with a pick (main band playing Skatepunk and metal songs).
This discovery has made me realise that if you play the same way for every song and try to get the sound you want downstream with thousands of pounds of amps and pedals you’ll never get the sound you are after cos there’s always another product you can find online that will supposedly do a better job.
Also you can spend months getting the perfect tone in your bedroom and it will probably sound like shit on a live stage, or at least not serve the band/music as it should do.
After 3 years of playing I’ve settled on my set up of a fairly simple amp and cab setup (which is normally set quite flat on the eq), my P bass, a decent well set up compressor to even out my janky playing, a tuner and a fuzz and chorus pedals. That setup covers so much sonic ground it’s crazy.
Good luck in your journey, and just enjoy the learning the music you love and playing with other people