As others have said, approaching this with the mindset of "this all needs to be rewritten!" is counter productive, and will set you up on collision course with leadership.
I inherited something similar 12 years ago, also cobbled together PHP, also no separation of code and rendering - making any sort of progress was painful.
As others have said there are a myriad of ways to extend code like this, encapsulating the old with a better facade. Splitting some pieces off - but it needs to be approached as a piecemeal project that takes a decent amount of time, but can be done in parallel with shipping new features.
I inherited something similar 12 years ago, also cobbled together PHP, also no separation of code and rendering - making any sort of progress was painful.
As others have said there are a myriad of ways to extend code like this, encapsulating the old with a better facade. Splitting some pieces off - but it needs to be approached as a piecemeal project that takes a decent amount of time, but can be done in parallel with shipping new features.