Yes, where are the amp and/or cab choices? I'm no expert, but I would definitely put that (or those) variable(s) in the top 3 in relation to the sounds I try to get. The only one of my projects to survive Covid has been using a multi room rehearsal rental place with at least 3 different amps and 3 different cabs that I have seen in 9 possible combinations. It is remarkable how different thse rigs sound. I have been lazy and using what is already there but am learning that I can only make 3 of the possible 9 combinations work to get the sounds I need. Technique, strings, and pickups/electronics/position all have a significant effect on my tone as well.
I've never seen a convincing argument for wood choice or specific hardware having significant impact on tone (unless the hardware didn't already do the job). I'm open to being proved wrong though. That said, more dramatic construction differences such as hollow vs. solid, or 35 scale vs. 28.5 scale would likely be more evident (if all else stayed the same).
I would also throw in that I would view fretboard wood choice as much more important than body wood choice on a solid body bass. Caveat: You could eq the sonic differences away pretty easily with the right amp. It might be harder to compensate if the 'feel' difference changed your playing style significantly.
Tone: Always a lot to think (OCD) about