How do you structure feedback for your devs so it’s the most constructive? Have you ever had a developer feel hurt or blindsided by critical feedback?

Feedback is always difficult to give constructively, and take with positive intent, in my view. I'd recommend taking the "continue" and "consider" approach, using evidence/scenario based rationale.

I.e. 
"continue": Behaviours you would love them to continue doing and build upon, and
"consider": Behaviours you would like them to think/reflect on and adjust to do things differently

For instance, I may say:
"The work you did on setting up the initial client engagement was outstanding. Taking a lead role in making sure that the team understood the scope and context, and then setting the scene clearly in the initial client session. Continue to take that leading role in proactive engagement.
When the solution was delivered, the client felt that they struggled to catch-up with you - consider taking a more proactive approach to business transition in future".

(bit of a top of mind example - but hopefully illustrative)

I try to get our team as close as possible to our clients and their feedback on the product. This allows them to understand not only what needs to change or improve but, more importantly, why it matters to the client and how it adds value.

By directly involving themselves in the feedback loop, developers build empathy, learn faster and take ownership of improvements.

To borrow a sporting analogy, it's important to play the ball, not the person.