What role does your engineering team have in prioritizing the roadmap for a product targeting developers?

Developers on the team will generally have a sense of the market since the products we build target them as a persona, especially if you're dogfooding your product. It's important to validate problems and solutions with customers to ensure that we're building a product that aligns with market needs, not just our own. I go into how to do that in another one of my answers. 

Product Managers on the team will build a complete picture of product priorities by talking to a diverse set of end users and analyzing the market. PMs should share insights with the team and give enough context in prioritization discussions to clarify why decisions are made. 

Quite a lot. But one has to be cautious in this and have PM exercise oversight, because not all developers are alike. Your developers may not accurately represent developers at your target customer. One can easily fall into the trap of assuming that the same pain points that your team experiences while using your product will be the same ones that customers prioritize. (By the way, it is very easy for PM to fall into the same trap.)

There is one universal truth, though, and it is that developers everywhere are annoyed by papercuts; both the developers working on the product as well as developers we are selling to. Therefore, we empower our developers to "see something, say something, fix something" for small issues without having to ask permission. This comes with guardrails in the form of a timebox. The contract is that if such a fix is going to tie up a developer for more than a couple of days, engineering should discuss it with PM first.