I wouldn't split the team just because personally I think it'll weaken the concept of the "platform team". Ideally what you want is people with different priorities/focuses within the team. Some on low level ops, others on high level APIs or services. Identifying who's skills fit what and letting them do that is key.

The other thing is just to split the category of work into 3 things; p1 bug fixes / long term projects / support work. Each week just make a note of time allocation for each based on what's happening (sometimes a p1 fix can take up the whole week). Try to minimise the support burden by creating office hours and defining SLAs for the rest of the company.

Make sure your team is not getting buried in support work. What's going to help them is just being able to filter out what's an immediate priority versus pushing off to tomorrow or the day after. Don't let them get bogged down or pinged constantly. Try to make that request flow async.

And most importantly, give them the time to accomplish tasks they think are most important. They are deep in the trenches and know what's going to be p1 vs not. Trust in their ability to guide the outcomes.