Sorry, I don’t know of a simple suggestion for you, but others may have better ideas. I don’t find too much for PHP use of Zoom, but there are certainly people using it and I’d encourage you to search for specific details and questions.
Probably first you’ll want to lay out the app design, maybe saying it’s coded in PHP, using JWT authentication to the Zoom REST API, to throw out a suggestion. (Assuming your client wants the integration done in PHP, instead of adding another technology such as node.js.)
So familiarity with those technologies will be key. Here’s a related post from this forum, and here’s what seems a good tutorial on calling REST APIs in PHP, using JWT authentication.