Valid code for method:
<?php

class Base { protected function foo() {} }
class Other extends Base { protected function foo() { echo "OK"; } }
class Child extends Base { public function bar() { $otherBase = new Other(); $otherBase->foo();  } }

$child = new Child();
$child->bar();

This might be a quirk how method inheritance works, as compared to how property inheritance works.  I think if you redefine a property in a subclass the visibility is re-restricted to that class.  For instance you can see: https://3v4l.org/j3aQg .  If you use the __construct to set the $this->foo, there is no scope issue.  Whereas with methods you're defining a signature that can be implemented in extended classes

So I don't know if this is a bug, per se, or just an oddity.  Someone with better knowledge on the intent on property inheritance could probably answer the discrepancy.

There are errors or assumptions that are wrong in your code.

What is wrong in my code?

In my opinion it is wrong that visibility works different for properties and for methods. If it is correct behaviour, please consider noticing this in PHP documentation.