What kind of questions should I ask each of them to learn as much as I can about the role and indicate that I'm an effective tech leader?
And then he walked into each of our offices and said "what do you need? I'll get it"
And he was suddenly our hero, our favorite manager.
So do that. Help them.
So my questions would cover those elements:
What is the decision making process at the team, how empowered are engineers to make their own technical decisions?
Are they learning anything new at work? Do they have challenges? Trying new things? Learning budget, learning groups?
Do they see the big picture? How is their everyday’s tasks contribute to the company’s mission? Are they proud of their work?
[0] https://en.m.wikipedia.org/wiki/Drive:_The_Surprising_Truth_...
Sometimes, you'll be taking a job that someone in the team thinks they should have been offered - but didn't for whatever reason (perhaps current management weren't aware... or they simply aren't appropriate skilled...)
These people can also be well respected by others in the team. And winning their respect is therefore particularly important, as they may be the ones to validate you on behalf of others.
You can normally spot them, as they will lean back, fold their arms and keep to themselves (out of frustration). Or act the opposite and be completely outspoken over the top of others.
I would consider that these people do exist, and need to be wooed in a slightly different way. Instead of asking 'what do you want?' perhaps it'd be better to ask 'where do you think the problems are?'.
If you could spend a month fixing/refactoring/changing any component of the system, what would it be?
What % of time is spent on planning/estimating/ vs. implementing, is this the right ratio for the team?
Edit: and make sure to check the restrooms. Employees take on the toilets and sinks all their frustration with the company ( break and soil things ).
But some more specific questions are good to start a conversation that can then follow it's own path. I like the questions in the other comment as starter questions.
I also like the Joel Test https://www.joelonsoftware.com/2000/08/09/the-joel-test-12-s... , but if they have a low score it could be judgmental and make them angry before your first day. Perhaps you can use it as a template to make a few assorted questions, without keeping an official score and not make all the questions if it's clear that they are scoring too low.
10/10 manager, would love to work with her again.