There are two main issues in your question. The first has to do with the use of mysql functions , that are deprecated and removed in new PHP versions , so of course every project that uses at least deprecated feature of a language is in serius problem.
The second is about following the procedural + functional (I guess) paradigm. Although I don't write PHP that way and I am really pro OOP PHP , I tend to think that if a project is consistent and well written the choice of what paradigm will be into has not a correct single answer. The quality of the code can be great even following a procedural + functional paradigm.
That means that neither every OOP PHP project is great , nor that every non OOP PHP project isn't great (wow, I hope that triple negative phrase makes sense) .
As PHP moves towards OOP (with many serius back steps in its way , in my opinion), writing PHP in a procedural + functional tend to be messy because they need to put some use of OOP inside (e.g. PDO or MySQLi) that leads to code that is a mix of almost all known programming paradigms and I can't think anyone that can keep that mix consistent and clean.
I think jkon expressed what most of use were thinking - although far more eloquently than I would have put it. I'd add that the UI is not really dependent on procedural/OOP. Of course we can get PHP to spit out HTML and even JS, but that's not really 'design'. The back end should be separated from the front end where possible. As soon as they are dependent on one another, problems with maintainability arise.
I'd also ask, why would you want to develop a project using dead functions? Makes no sense at all. If you wrote a sports column using Medieval English, you'd be called a weirdo.