git push
can push all branches or a single one dependent on this configuration:
Push all branches
git config --global push.default matching
It will push all the branches to the remote branch and would merge them.
If you don't want to push all branches, you can push the current branch if you fully specify its name, but this is much is not different from default
.
Push only the current branch if its named upstream is identical
git config --global push.default simple
So, it's better, in my opinion, to use this option and push your code branch by branch. It's better to push branches manually and individually.