For me, I guess there are five main buckets of themes to describe the TMNT.
The first would be the desire for vengeance against Shredder for killing Hamato Yoshi. In a way, their entire lives up to the point where they are first introduced to the audience was just training to prepare for that showdown. This aspect of the turtles is often overlooked.
The second would be, as you described, just survival. Just trying to stay in the shadows and lay low, avoiding unnecessary conflict.
The third would be themes of identity, finding themselves, and trying to make sense of the consequences of their mutation and isolation in the world.
The fourth are the obvious themes of family.
And lastly could be summed up with the quote "I love being a turtle." It's just themes of acceptance for who they are and the enjoyment of being mutated turtles.
