The Product is the Business. The User Problem is the Essence of the Product.
Products with uncontrolled technical debt are a pain as soon as you want to add or modify even the smallest feature. No matter how good they are, your developers will just struggle in getting your user stories "done".
Sorry if you're a Product Owner and that you feel you're doing the same than a Product Manager. Either you're actually not, or your company didn't give you the proper job title. And then I strongly encourage you to settle that.
This post is not about Agile. It is about getting things done. And it is about a process that serves business objectives. Understanding your context is key in selecting a methodology, so that you can then embrace it, and finally make it yours. In that specific order.
A Way to Product Management 