1. Who watches for security advisories?
"The IT person" isn't enough. You need a name, on your team or at your provider, who hears about an advisory like this the day it comes out and knows whether it affects you: that your site runs on PHP, and which version.
2. Who updates it and confirms in writing that it's done?
A "we're good" over the phone doesn't cut it. Ask for written confirmation with the exact PHP version installed (for example, 8.3.36 or later on the 8.3 branch), the date, and proof that PHP was restarted so the new version is actually running. If someone only applied a temporary measure, they should tell you in those words.
3. What do you do if your site runs on a version that no longer gets patches?
If your site is on PHP 8.1 or older, those versions no longer receive updates from the PHP project. Given the severity, the PHP security team provided minimal source-code backports for PHP 7.4, 8.0, and 8.1, meant for people who build PHP from source or don't have an LTS (long-term support) vendor; some distributions and LTS vendors also provide their own backported fixes. That's a lifeline, not a plan. The real plan is to migrate to a supported branch (currently 8.2, 8.3, 8.4, and 8.5), and that needs a budget and careful testing. If you're on 7.3 or older, there isn't even that minimal patch.
And if you're on 8.2, there is a patch this time (8.2.35), but that branch loses support on December 31, 2026. Now is a good time to put the migration on the calendar.