Can't login via SSH when Github and Bitbucket usernames are the same

[nikronys]

I have the same email and username of github and bitbucket accounts. I can easily add my github account and it works smoothly. After I add the bitbucket one and try to clone a remote repo, I get this error:

Please make sure you have the correct access rights
and the repository exists.
Forbidden

fatal: Could not read from remote repository.

It doesn't throw any authentication errors, so creds are fine. The only thing I can do right now is to see my public remote repositories. In the bitbucket SSH keys settings, I see Never used in the Last used column. Moreover, I've removed .ssh folder and set up everything from scratch - doesn't work. I've also tried to generate Bitbucket SSH key myself - doesn't work.

I also have a default Bitbucket account and it works perfectly fine.

Mac OS 10.15.2
Sourcetree 4.0.1
Embedded Git 2.23.0 (in use)
System Git 2.24.1 (switching doesn't help)

[ssulun]

Try adding the following lines to your ssh configuration file. In my Ubuntu, it is ~/.ssh/config

Host bitbucket.org
        HostName bitbucket.org
        PreferredAuthentications publickey
        IdentityFile ~/.ssh/id_rsa