What search engines actually do with it.
WHAT IS TRUE
Search engines prefer secure sites. HTTPS is a ranking signal, though a small one compared with content quality and relevance.
Browsers marking a site as not secure costs you visitors regardless of ranking, which matters more in practice.
WHAT IS NOT TRUE
That a paid certificate ranks better than a free one. There is no difference. That extended validation helps ranking. It does not. That a dedicated IP helps. It does not.
WHAT ACTUALLY MATTERS FOR A MIGRATION TO HTTPS
Redirect every http URL to its https equivalent with a 301, in a single hop Update internal links so visitors are not sent through redirects Update canonical tags Update the sitemap Add the https property in Search Console and submit the sitemap Update any external references you control
DONE PROPERLY
Rankings transfer with no lasting loss. A short-term fluctuation is normal while search engines recrawl.
DONE BADLY
Missing redirects lose the ranking accumulated on those URLs.
