Here are some from a text file I keep around for these purposes:

• What has your team been working on recently? What new changes have you shipped in the last six months?
• What is the biggest difficulty your team is facing right now?
• How long has the team existed and how long have you been managing it?
• Is the team all remote? Are you?
• How long does it take for code to be deployed after being committed?
• How often do team members move teams?
• What kinds of (soft or hard) skills do you need most on the team right now?
• Do you have a defined onboarding process?
• How long does it take for people to get up to speed as new hires? How much would a new hire be doing in six months?
• Does the team maintain deployment infrastructure? Production infrastructure? Is there an on-call rotation?
• What does your planning cycle look like? Scrum? Kanban? Meetings?
• What’s one thing you would change or improve on the team if you could snap your fingers?
• What would you like to be doing less and more of on your team?
• How does the product representative interact with the eng team?
• Do you have a career ladder, with levels, and expectations at each of the level defined?
• What is your performance review cycle like? 1:1s?