When I was working in an office environment, not from home, I often could ask around for advice, get a hint about approaches to different people. It was more of a challenge when remote only.

They don't even sound that shitty to me. Managers like everyone else in the world have to work within the constraints of the system in place. Like Scrum vs Kanban. Maybe the manager couldn't care less but their director is the biggest Scrum cheerleader ever. And maybe they're getting hounded for the estimate and just need a number. And maybe skipping the internship program looks bad for the manager. And so on.

Even if it's all the Manager's fault there's far worse sins in the world than dictating a methodology or asking for an estimate.

Its only significance seem to be that this might be one of reason why manager did not liked op, which yes, can happen with some personalities. But, op does not provide any part of story that would show that.

Yeah. If it's something I have some familiarity with, I can usually throw out an upper bound. And do as you suggest and/or say "If you want me to spend next week digging into the details a bit more deeply I can, but it means I won't be spending much time on my current project. Your call." (And perhaps the estimate is important because of a product launch etc. Or maybe it's just a number on someone's status report.)

The reality—if you give me an estimate, I am probably going to fatten it up even further when I pass it up the chain, not because I don’t trust your estimate, but because something always happens outside of your and my control.