I run my photography website with a VPS, but I'm looking to expand my offerings through a third-party photo hosting service Pixieset. Pixieset allows users to connect their Pixieset account/galleries to a custom domain so that clients don't have to visit two different websites/feel like they're "leaving" the photographers website.
For the sake of example, my website URL is example.com. Let's say I create a subdomain galleries.example.com connected with Pixieset.
My question is, will linking visitors to this external host as a subdomain from my own website via menu link result in SEO penalties for linking externally? HostGator says "Your subdomains will be treated as entirely separate websites in the eyes of Google.?" (source: https://www.hostgator.com/blog/what-are-subdomains-affect-seo/)