I created a new private repository and added my ssh key under the project ssh keys.
I couldn't push my local data into the repository - always getting this git error:
git@bitbucket.org: Permission denied (publickey).
fatal: Could not read from remote repository.
I finally came across a random (not accepted) answer to a question for this error message, that told me to add the key under profile instead of project - that worked.
So my question is, what do keys under "project" do, if they don't allow you to push commits?