If you have a website, here are some design and technical aspects you should check or confirm with the developer.

Design and Functionality:
Meta tags/Metadata for every page
Contact Form Testing
Favicon Icon
404 Page
Images/Media Alt Texts
Images Optimization
Speed and Performance test
Device compatibility
Browser compatibility
Search engine compatibility
Responsive Design
Optimize CSS, Scripts and Validate
Internal & External Links
Header Logo to Home Page Linking
External links open in a new tab
Automatic Cache clear
Redirections
Cookies policy notice
Get CDN if possible

Security:
SSL certificate
Site Health
Privacy policy and Terms page
Database Backup
Easy reCAPTCHA
SMTP
User roles
Remove unwanted Scripts/Plugins
SEO:
HTML and XML Sitemaps
Robot.txt file configuration
Analytics Setup/Linking
Google Indexing/Crawling
Google business profile
Google Search Console
Broken links fix
Schedule:
Storage and C-panel
Complete Site Backup
Renew Checks for Domain, Hosting, SSL, etc.
Cache clearing after any updates
Plugins Updates for WordPress sites