How do you build a team that can both handle day to day customer issues and keep time for innovation/discovery?
It's easy for teams to over-index on day to day customer issues and lose sight of innovation; the opposite is unlikely. If your team has customer focus figured out (if not, tackle that first), there are three things that have worked well for my teams to keep the balance:
Every member of the team (especially junior!) understands and can speak to the big picture product strategy and market
Intentional and structured approach to include customers into discovery (vs letting them always drive the agenda when speaking with them)
Incentives to innovate
Why does this matter?
Big picture thinking: before you can ask the team to "innovate", you need them to fully understand the playing field - where does your product play, why do you win, who is it for etc. Too often junior team members don't even fully comprehend what the product does or what is the strategy overall, and leader do not invest time into educating the team repeatedly. As a result, the team won't have the right information to even have "aha moments" and spot the new opportunities that lead to innovation. Bonus points if you not only communicate strategy to your team repeatedly, but also empower more junior team members to present said strategy to customers - this will increase their comprehension and comfort with it, thus empowering them to explore its gaps/boundaries and innovate.
You don't have to always listen to customers: In fact, most customers appreciate listening to you, and providing feedback on your future/ideas, rather than telling you what's working or not working now. However, it is easy to fall into the habit of letting customers fully drive the agenda of the meetings between them and the PM team, always making a "listening session" or complaints about bugs, feature requests etc. An easy way to break this cycle is to create programs around discovery, new capability testing, design feedback sessions and the like - customers will be happy to participate in those structured sessions, especially if you have already established their trust that and practiced listening to them. Lots of ideas to explore and innovate on will come from those sessions.
Incentives: As a team leader, you'd have to have a clear definition of what do you see as innovation (is it novel ideas for building new capabilities? Suggestions on how to expand into new use cases? Experimentation? Something else?), and once you share that with the team, you need to track and celebrate behaviors and outcomes that are associated with your definition of innovation. A lot of innovation programs, especially in big tech, do not pick up because teams see no good reason to spend time on those vs something else. And, since innovation often has a risk of not working out, it's important to incentivize not just outcomes, but also behaviors - e.g. "we tried 5 ways to improve X and none of them worked" deserves recognition and not being frowned upon.