It'd be nice to hear from one of our highly talented luthiers here because we're getting into nuances where their advice might be very helpful...
Short of that, here's my player/maintenance-minded thinking about notch depth, related to sanding the top of the bridge down after adjusting the notch depth...
It really depends on what the bass is used for. For primarily arco, it's good if the strings only barely sit inside their notch, meaning that the bridge top has been sanded leaving the new notch very shallow. For serious pizz, or even more so with slap/pizz -- and especially if the strings are low tension -- the strings have to sit fairly deeply in their notch or they'll slip out with playing, meaning that the notch has to be relatively deep. That said, a deeper notch should also not be so narrow that it entraps the string, deadening it.
And lastly, deepening notches and sanding the bridge top down does have the potential to change the tone because the string tension may be lower, and because the vibrating/transmitting mass of the bridge is reduced. The same goes for sanding the feet of a bridge to improve fit on the top. So this work needs to be done sparingly.
Given all that and given that the human ear -- and the mind behind it -- is very subjective, it's best to always assume that any change changes tone.
Luthiers, because they do this work all the time on a variety of bridges and basses, have a sense for what is right related to keeping the strings in place while playing and related to the tone quality.