Leave it alone if
- The site is not self-hosted WordPress. Pages edited inside Squarespace, Wix or Shopify run on the platform's own software, so this plan has nothing to look after. Shared hosting is the right product for a hand-built HTML or PHP site.
- The theme was customised without a child theme. Unattended updates are riskier there rather than safer, because each one can overwrite work somebody paid for. Get a child theme in place first.
- The domain and hosting are still held by a former designer. Settle who owns those accounts before you buy a plan you cannot log into.
- You are replacing the site soon. Put the new build where it is going to live and skip the move in between.