This website isn't live yet. This website hasn't been launched yet. This website isn't publicly available yet. This website isn't available to the public yet. This website can't be accessed by the public yet. This website is still in beta, it isn't live yet. This website is still being tested, it isn't live yet.

hasn't benn released to the {public,users} of internet

We would only use "released" when talking about software or mobile phone apps. It isn't normal to say a website has been released.

My choices: "... launched on the internet." or "... been uploaded to the internet.".

My choices: 1st = launched / 2nd = activated / 3rd = made available to the public