Thanks for reaching out. I have passed on this feedback to our Bitbucket Cloud team. I will let you know in this thread once I have an update on this from the team.
This was removed from v2 due to some security concerns. If this feature is needed, our team will have to take a deeper look into it to come up with a solution.
I think you can use access_tokens (see section 5 - Bitbucket Cloud JWT Grant (urn:bitbucket:oauth2:jwt)) to both pull and push git repos. A bit further down on that same page it describes repository cloning, but if the branch permissions are set correctly you should be able to push as well.