Issues connecting to Github using ssh key

[luca_amerio]

I have a repository on Sourcetree connected to two remotes, one on Gitlab and one on Github. I set up the same ssh key on both websites and loaded the private key in Tools>Option>General>SSH Key. 

However, while I can Fetch, Pull and Push from the Gitlab remote, every time I try to do one of these actions from the Github one, the Credential Helper Selector pops up. I think I tried all options there, but with no luck. Also, since Github is not using credentials login since August 13, 2021, I'm not even sure the CredentialHelperSelector is of any use here.

For the sake of completeness, I have two different usernames on Gitlab and Github. I'm not sure if this could be the cause or contribute to the problem.

Could you please help me understanding what I'm doing wrong? This issue is really driving me crazy