Solution
Got mail response from Taylor on support mail. I attach the response for your future help:
"Most likely it has hit a prompt while trying to clone the repository. I would delete the site and try again. If that doesn't work, you should SSH into the server manually and try cloning the repository and running composer install to make sure you do not hit any prompts. Bitbucket is probably asking you to accept a new SSH key."
I cloned 1 repo from Bitbucket and accepted fingerprint, deleted it again and afterwards I could use Forge. Thanks!
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