Your team and the company seems to be pretty healthy. It sounds like a real good basis for fostering some change. Many others are struggling with the environment already, so you can be happy about it and focus on improvements.
What is your team thinking about the the demission of your Head of IT? Do they share your concerns about health of the backlog and requirements?
If you not did so already, I would setup a dedicated session with your team. This should not be one of your “standard” meeting, as it is about creating a sense of urgency to implement changes in your team. You might want to invite the PO as well, as the change will affect him as well. Literally he is part of the team as well. Use this session to let everyone in the team (including you) share their concerns. You should (have) come up with an align sense of urgency from it.
If you have created a common understanding, I would start to look for the key stakeholders, who are affected most and can be drivers of a change. You will need their support if you want to transform the way the team is working. Collect the expectations and start to plan actions with them, which will lead to a change addressing your concerns.
Now it will be your task to take action to ensure that the plan can be implemented. If you find out, that you are lacking skills or capacities, you might talk to you management about the successor of the Head of IT. You should be able to deliver concrete requirements by then, as you know the demand and the urgency. You should also can think about bringing temporary support to the team from a trainer or subject matter expert, if the team raises concerns being able to deliver. Finally you should make the change a regular topic of your retrospectives, as you will have many learnings with you and your team. Make sure they are considered continuously and you improve based on them.
All in all I think it is a real nice challenge you are facing. You have the chance too learn a lot new things about you and your team right now. I love this kind of chances as you can make use of them to become better. Sorry for your former Head of IT, but he probably did a big favor to you.
P. S. if you look for a book, I would point you to “Leading Change” by John P. Kotter. Since this book has been written, there seems to be a widely accepted understanding how change works and how it has to be implemented. It would give you a deep dive into what I just sketched out above.