IXR -32300: transport error

I’ve copied site to a new place. Just in case re-installed the jetpack in the new site (deactivate, delete, install). When setting it up I get the following error:

Error Details: The Jetpack server was unable to communicate with your site [IXR -32300: transport error: http_request_failed cURL error 52: Empty reply from server]

I’ve already checked https://jetpack.com/support/getting-started-with-jetpack/troubleshooting-tips/, no help.

The error is also listed here: https://jetpack.com/support/getting-started-with-jetpack/what-do-these-error-messages-mean/

For me it seems that jetpack somehow still thinks that there should be a connection since it existed in the old site. How do I properly remove the jetpack and get so to say fresh installation? Thanks.