From what I’ve seen, the action will always have a slow increase from nut to bridge, and that’s pretty essential. Be aware that if you lower the bridge, you may also need to adjust the height of the pickups, and you’ll almost certainly need to adjust the intonation. It also may be an issue with the truss rod and how much bow is in the neck. I’m a beginner though, so I’ll leave other comments to experts!
After watching a bunch of videos I did my own setup on my Schecter Studio-4. I adjusted it to something that seemed good for me. Then I took it to a local shop run by an ex-pro musician. He looked it over, said he really liked it, then he plugged it into an amp and sat and played it in different styles for about 15 minutes. I was happy that he ended up endorsing my setup, but we also talked about options for changing it if I wanted to focus on different styles.
So… avoiding the question of what “digging in” means to different people, have someone who really knows how to play bass (not just adjust them!) play on your bass with you. Then talk to them about the action and what they like/dislike about it, and how that relates to what you want.
Another thing is that I had adjusted my neck very flat - so flat that when I changed from a dry mountain environment to a wet seaside environment, I started having buzz problems - turned out the bow on the neck had flattened out totally. A quarter turn of the truss rod cleaned it up. This wasn’t an instant effect - it took place over a few days while I started becoming increasingly frustrated trying to figure out what issue with my technique was causing the problem. Until I figured out that it wasn’t my technique, but that the setup had changed due to warmth and humidity.
Finally, I was incredibly apprehensive about doing my own setup. But I know that as I get more experience, what I want will evolve and I don’t want to be dependent on someone else. If I want to try something new - different strings, different action, I don’t want to have to schedule a trip to a shop. It really is pretty fast and easy, and will just get faster the next time. I was super careful adjusting the truss rod in small increments. The worst that can happen if you’re careful is that you end up taking it to a professional anyway. And the best is that you’ll have the confidence that you can tweak things if you decide that you want to raise or lower the action or adjust different strings, and you can fix it if the environment changes from 6500 foot mountain-dry to sea-level temperate and humid!