Your team isn’t working well with the product team, or the design team, or another tech team, and the lack of collaboration is dragging everyone down. There’s no quick fix here, but showing a willingness to improve collaboration goes a long way. If you aren’t already, make sure you’re having regular touch-bases with the appropriate peers to work through issues. Gather actionable feedback from your team, and have productive conversations about possible improvements. You can make the situation worse by undermining your peers in front of your team, so even when you are frustrated with them, try to stay positive and supportive of their efforts in public.
If your team isn’t working well together, look into creating some opportunities for them to hang out without it being all about work. Taking the whole team to lunch, leaving work early on a Friday afternoon to attend a fun event together, encouraging some PG-rated humor in chat rooms, and asking people how their lives are going are all ways to cultivate team unity. As a new manager I was pretty reluctant to get into this type of bonding, but even most introverts want to have a feeling of relatedness with their team. Assuming you don’t have any of the “people drama” problems listed earlier, small efforts in this area can warm the group up considerably.