Any updates marked as a Security update should be applied as soon as possible.
Security updates by the Drupal Security Team are announced here and, since Drupal is open source, failing to patch your site leaves you open to attacks because people can look at the content of the security announcements and find the vulnerabilities in your site's code. This is why it is important to patch immediately.
Now, not every announcement requires immediate action; to find out how soon you need to act, you have to actually read the security announcements for core/the relevant contrib module. In many cases, there may only be a security problem if users have certain permissions, and if you only have admins and anonymous users (a common setup), you may not have to do anything in that specific case.
In your case, based on the list of modules shown, Entity Print has a security update, which was fixed in version 2.5, which was released on April 11, 2022.
This means that your vendor has ignored an important security patch for over half a year-- pretty terrible performance for which there is not really an excuse. So as @Kevin said, I would find a new vendor.