Hello everyone, i built a new wordpress site (10ish pages, 600+ blog posts) for a client on my own hosting (siteground) using a temporary domain. Their old site and domain is on bluehost.
They want to now host the new site on siteground (probably using my hosting), and they’re looking to transfer their domain to somewhere else like GoDaddy (because bluehost domain fees are crazy). [Their bluehost costs are insane]
I want to know what is the best way I should go about linking their domain to the new site. Are there any best practices? Should I simply put their domain on the site I built or should I copy the new site and link it to a new website on my host.
I’ve never done this for a site with this much content, and I’m also not sure what will happen the to SEO (i’ve improved the seo on each article as the old developer didn’t use categories, tags, h1/2/3 headers, etc).
I’d appreciate this communities help and thanks in advance for taking the time!

Transfer the domain name, update the DNS records and make sure the old URLs redirect to new ones to keep SEO
If they require a new hosting and not yours, migrate the website files and database to their hosting
The new vendor should transfer everything to you new hosting, both mails and website. the only thing he/she need is cpanel credentials of the old site. You are also required to create website backup using available plugins such all-in-one migration to restore the website to the new hosting yourself if that doesn’t at the new vendor level
For cleints use namecheap.com for domains. It’s much cheaper. Then just have them add you as a user / team member