So I haven’t used Resolve for sound, but Premiere isn’t primarily designed as an audio editing platform, and I doubt the new additions to Resolve make it a “proper” audio program, either. I’d say the most important thing is to work with what you’re comfortable using. If you can get similar results between Resolve and Premiere, but you prefer the Resolve workflow, that’s more than enough reason to pick it.
The program should be okay for simple to modestly complicated sound if you have decent volume controls, and some basic effects like EQ and limiters. “Conventionally-speaking,” you typically hand off the audio to a separate sound program like Pro Tools or Audition (which is a class of software called a “DAW,” or “digital audio workstation,” which is an overly-complicated way of saying it’s a program that basically emulates the functions of an old-school physical mixing board). However, this isn’t necessarily appropriate for all projects, so I’d again just say work with what works best for you! If you hit any limitations or get curious about what further options you have available audio-wise, then you can look into Pro Tools. It might be equivalent to doing color correction in a really basic video program versus the more robust options in Resolve; audio can open up a lot too with your available effects, track count, and overall workflow speed, once you migrate to a dedicated program.