I don’t see why you couldn’t, and I’ve seen other people on this sub do it. As long as you can work out the availabilities at both locations to not conflict, there really isn’t a reason to tell your manager. You don’t need their permission to get a second job, and it’s honestly none of their business (again, as long as you can work out the availabilities not to conflict)

yes you can Tarbux is licensed by Target so pay and benefits come from target and you would be a target employee working in the starbucks dept.

You should talk to your manager about it.