The "we're like family" phrase can mean many different things in the work environment, so don't read too deeply into it.
That being said, it's often a sign of poor management; managers will use "we're like family" instead of addressing problems that they need to address. It can create a very stressful situation if you're a high performer, because the expectations and handholding quickly get unreasonable.
(The song "Surface Pressure" from Encanto explains the situation exactly.)
For example, I once worked with a manager who used the "we're like family" excuse when incoming tickets were incomprehensible and missing critical information. He was just copping out of his job, which was to set processes and make sure new employees knew the processes. Instead, his expectation was that I would handhold the organization through the ticketing system.