That’s a very very good question about accessibility. We usually don’t design for users who zoom using the browser zoom function, that’s considered an edge case. Most designers will ditch fixing such an issue, by not considering it as a bug. But zooming is important for a fair share of the older part of the population. They’d be better of setting a different solution in place, such as increasing the general resolution of their operating system, but we can’t put that on them because that’s a technical thing to do and OS are often not doing a great job at explaining it (macOS kind of does though).
Your client is right asking that you look for a fix.
Can you please relink your CMS content? The link leads to a 404, and I can’t find a page where I can reproduce the overlapping.