If a plugin generates output during activation, activate_plugin will return an WP_Error object configured like this:

$output = ob_get_clean();
return new WP_Error( 'unexpected_output', __( 'The plugin generated unexpected output.' ), $output );

As you can see, the output is passed as the third parameter, and the error has code "unexpected_output".

I have a use-case where I need the output that was generated for logging reasons.

Relevant code that should print the output: