In my opinion, and leaving aside the design and visual aspects of any website, any webmaster should take into account new developments and standards in terms of programming languages and their versions. Not only to ensure the correct operation of the site, but also an efficient functioning by upgrading any part of the code or even whole files to adapt it to the new environments (hosting, browsers, etc.).
If you do not manage a CMS – which usually include automatic update information and utilities – you should contact your hosting to request for information on the issue.
Even static HTML-CSS-based websites should be updated (and upgraded) periodically to include new features and technologies to meet their specifications and desired objectives.