Focus and think of any other improvement you could do.
It sounds like management doesn’t think there is an actual problem to solve, so I wouldn’t necessarily pick refactoring or rewrite as the hill to die on.
If you go the refactoring route, i have little advice:
0. Clean up the database, it will immediately impact performance and make management happy
1. Find vertical (feature-wise) or horizontal (layer-wise) architectural boundaries and split the code base into module, separated libraries. This will be an ongoing process for a long while. Do it by touching as little code as possible - this is pure scaffolding, actual refactoring comes later.
2. Stick with PHP, at least until results from #1 aren’t good enough.
3. Use testing as a tool to pressure management, it works a surprisingly large number of times
4. Rewrite one feature/page at a time, once results from #1 indicate a good candidate. It might be a good idea to introduce a new language at this point, or even some form of micro services (if it makes sense).