1 Product, Multiple Adhoc Projects, 1 Scrum Team

Suppose the team said no, because of the focus issue you describe, and asked probing questions about the outcomes management were trying to achieve. How would management respond to that position? 

As a Scrum Master, why would it be up to you to reorganize the team?  If there are problems, the Developers should be able to reorganize themselves in a way to make the work possible. And if they feel it's not possible, they can let the Product Owner bring it to the attention of others outside the team. You can help people understand the Scrum framework, how it can benefit the organization and support the Developers in their efforts. 

Your "management" doesn't seem to understand how their demands are negatively impacting your team's ability to deliver value. 

How can i reorganize them in such a way where the product team can solely focus on the product and adopting scrum, while the other IaC projects can be run in other Agile formats?

You can may be have some of the team members focusing on IaC which means they are not involved in the product development sprints (you may utilize them for some peer review or testing). Let the other members focus on the development sprint. This way you can bring about some kind of focus. It is important to inform the management about this arrangement and the reason for doing so.

@Daniel Wilhite,

As a Scrum Master, why would it be up to you to reorganize the team?  If there are problems, the Developers should be able to reorganize themselves in a way to make the work possible. And if they feel it's not possible, they can let the Product Owner bring it to the attention of others outside the team. You can help people understand the Scrum framework, how it can benefit the organization and support the Developers in their efforts. 

Your "management" doesn't seem to understand how their demands are negatively impacting your team's ability to deliver value. 

The developers have raised the concerns of losing direction due to multiple IaC projects. Initially, the team was set up just to focus on development of the product.

It has been brought to my attention and I had raised this to the Product Owner. Interestingly, the PO is also the lead for the IaC projects.

I have brought the Scrum Framework up, and how it should be product focused based on empiricism, instead of project focused. However due to manpower constraints, it seems like there is no other way other than combining all source of work to 1 single 'work backlog'.

The management understands the negative impact in our team to deliver value to the product, but have no other choice. 

@Anand Balakrishnan,
You can may be have some of the team members focusing on IaC which means they are not involved in the product development sprints (you may utilize them for some peer review or testing). Let the other members focus on the development sprint. 

I do agree and have given some thought about this. However after seeking inputs from the team members and PO, the IaC projects require a significant amount of resources, and it seems for now the best way forward is to combine all related projects work into a single backlog. 

In sprint planning, we will then prioritize accordingly based on this source of truth, with PO and team members agreement. Do let me know your thought on this. 

In sprint planning, we will then prioritize accordingly based on this source of truth, with PO and team members agreement.

Might be the best way forward for you now based on the constraints. One good thing is the PO is involved in both areas the project and the product. Let him/her play a key role in prioritizing the work. As a Scrum master you have to guard the team from burnout and also help the PO to prioritize. I would also suggest having a backlog refinement session once every sprint so that you keep tasks ready for your sprint planning.

I would also suggest having a backlog refinement session once every sprint so that you keep tasks ready for your sprint planning

Indeed. This would keep the backlog ready and prepared for the next sprint. 

The extra information is helpful. 

What kind of Sprint Goals are the team creating?  That could help to keep the team focused on the work that is most important for the Sprint. It's not unusual to have work in the Sprint Backlog that isn't in support of the Sprint Goals but does provide value to the product and stakeholders. Create a Sprint Goal, pull items from the Product Backlog that will satisfy it, then include IaC items that can be done. Help the Developers remain focused on getting the goal supporting items first. 

With Sprint Goals, the team can set a focus on IaC in one Sprint and product enhancement in another. But they can continue to do work on both.