To have someone's back means to "always be ready to defend or help someone."
So by extension, "we got each other's backs" is a way of saying that you and another person are both ready to defend and help one another in times of need.
What I want to know is whether "we got each other's backs" can be shortened to “we got each other” without changing the meaning.
The reason I wonder this is that "I got you” has the same meaning “I got your back.” Can this shortening be extended to the other phrase as well?