Is it an SEO problem if I change an SSL certificate from that of a large web hosting company to one that is free software?

Oh Yeah... It started back in 2014

We’ve seen positive results, so we’re starting to use HTTPS as a ranking signal.

SEO ranking is also improved, as search engines like Google favor sites that use HTTPS over HTTP. This protocol is indicated in the address bar of the browser with a padlock icon or a green label, and search engines recognize these sites as more trustworthy and relevant.

SSL/TLS Certificates: How They Boost Your SEO and Trust?