After that it's just part of the conversation. Probing the resume. And asking some of these question flat out. I also discuss real practical problems/challenges we have at work, most of which require a team to work together.
We also (used to pre-covid) take the person for lunch and decidedly talk not about work at that time.
Of course it's different between an engineer fresh from college and a seasoned software engineer or architect.
In the end, I think interviewing is itself a skill one needs to train. Just having a person solve some brain-teasers doesn't cut it. I have _way_ more teams, co-founders, etc, fail due to social issue rather than technical skills.
And I am by no means presuming that I'm good at it, just that these are things I look for.
An important part I forgot to mention in the first post that the person is interviewing the company as much as we interview the person. So we leave a significant amount of time for asking questions about the company... and try to make a good impression.
(Sorry for the essay.)
I'll spoil a bit of the book though. Free form "coffee interviews" or lunch interviews are the worst possible types. They introduce a ton of bias into the process that's not related to job performance.