If you are of the opinion to transfer your website from HTTP to HTTPS and you have parameter handling located in Google Search Console, then ensure that you migrate parameter handling set while you migrate to HTTPS.
Hence, you have to make sure you set up a new Google Search Console verified property for your HTTPS site. Also, you have to make sure that you set up the parameter handling in there as well. As per a recent tweet from John Mueller, one needs to transfer the parameter handling settings in case you are moving to HTTPS.
There are specific complexities around any site migration in the form of legacy configurations. These legacy configurations need to be handled and documented during the process of movement.
See some discussion at Twitter.