What to check before launching the site

Applies to both cases - with one important difference. When redesigning an existing site, the technical SEO points (301 redirects, URL structure maintenance, canonical) are more critical than when starting from scratch, because you have something to lose: existing positions, inbound links and indexing history. With a new domain, the main risks are improper analytics setup and too early or too late sitemap submission to Google Search Console.

Preferably both, each his own part. Technical sections (SEO, performance, security headers, redirects) should be reviewed by a developer or technical person with access to the server and CMS. Content sections (text, contact information, legal policies, forms) should go through the owner or editor - because the developer often doesn't know if the phone number in the footer is up to date. Checklists, where one person is responsible for everything, have a higher percentage of missed points.

Focus on critical points - those marked in the list as blocking the launch. The rest are tasks for the first 7 days after launch. Never put off until "after" three things: noindex must be turned off, analytics must collect data from the first session, and checkout (if applicable) must be tested with full flow. Lost analytics data from the first few days after launch is irrecoverable - the only truly irreversible consequence of a rushed launch.