Question: How do you navigate such questions? I feel like I ethically can't share non-public information with competitors. But their HR was pushing hard for more detailed info that I basically refused to share.
In the current market, I don't have a lot of options so I'm between a rock and hard place. What do?
Yep, say that. If they don't accept it, walk away.
If they keep pressing, walk away, man. That's just setting yourself up for a protracted legal battle between the two companies, and the new employer would probably throw you under the bus as soon as it happens ("We'd never do something like that, the new guy volunteered the info!")
If you actually have a NDA, now's the time to use it. If you don't, but feel icky about it, just be firm that you can't share confidential information. It's not worth sacrificing your professional and personal integrity.
Worth calling them out,
I'm ethically and contractually bound not to disclose specific details around this work.
At a high-level I'm doing A)B) & C.
I imagine you expect the same standard from your team members.
Then turn the questions on them-
Relative to this role, help me understand what you're trying to accomplish.
What are you priority needs/wants? What does success look like?
As for your Job Search -
Don't focus on companies and openings.
Instead, look for the guy you can best serve.
There's a Senior Manager/Executive out there who needs your help.
On this, Linkedin Profiles are actually a useful tool.