If the key is in ~/.ssh and named id_rsa (or id_dsa, if a DSA key), then the private key should not need to be specified. Phillipp wasn’t specifying the key when it was successful, so the key must be named id_rsa. Here’s a reference with a much better explanation than I can give 
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So the question is: is there a home directory for user openhab?
Very good point! The manual installation instructions specify creating the openhab account using --no-create-home, so odds are very good that the package installation process does the same. I’ll update my previous post.