If it’s a WordPress site, I wouldn’t transfer the whole hosting account just to hand the site to someone else. I’d normally create a full backup of the files and database, then move them to the buyer’s hosting and update the domain/DNS after testing.
For a clean handover, I’d include the database, wp-content, uploads, configuration details, SSL, cron jobs, and any DNS records they actually need. Before changing DNS, I’d test the migrated site on the new server so there’s no unnecessary downtime.
If the site is small, a migration plugin can make it simple. For a larger site, I prefer a manual files + database migration because you have more control over what is being moved.