[BUG]: Docs bug fix/improvements for inherited overloaded virtual methods

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What version (or hash if on master) of pybind11 are you using?

master

Problem description

Consider the documentation: Inheritance
If we add a virtual function overload, then the compilation fails.

class Animal {
public:
    virtual std::string go() { return ""; } // Added virtual overload
    virtual std::string go(int n_times) = 0;
    virtual std::string name() { return "unknown"; }
};
class Dog : public Animal {
public:
    std::string go(int n_times) override {
        std::string result;
        for (int i=0; i<n_times; ++i)
            result += bark() + " ";
        return result;
    }
    virtual std::string bark() { return "woof!"; }
};

template <class AnimalBase = Animal> class PyAnimal : public AnimalBase {
public:
    using AnimalBase::AnimalBase; // Inherit constructors
    std::string go() override { PYBIND11_OVERRIDE(std::string, AnimalBase, go, ); } // Added virtual overload
    std::string go(int n_times) override { PYBIND11_OVERRIDE_PURE(std::string, AnimalBase, go, n_times); }
    std::string name() override { PYBIND11_OVERRIDE(std::string, AnimalBase, name, ); }
};
template <class DogBase = Dog> class PyDog : public PyAnimal<DogBase> {
public:
    using PyAnimal<DogBase>::PyAnimal; // Inherit constructors
    // Override PyAnimal's pure virtual go() with a non-pure one:
    std::string go(int n_times) override { PYBIND11_OVERRIDE(std::string, DogBase, go, n_times); }
    std::string bark() override { PYBIND11_OVERRIDE(std::string, DogBase, bark, ); }
};

Now this won't compile!
So since we are registering every virtual method for each class we should explicitly use the base class like the following:

template <class AnimalBase = Animal> class PyAnimal : public AnimalBase {
public:
    using AnimalBase::AnimalBase; // Inherit constructors
    std::string go() override { PYBIND11_OVERRIDE(std::string, Animal, go, ); }
    std::string go(int n_times) override { PYBIND11_OVERRIDE_PURE(std::string, Animal, go, n_times); }
    std::string name() override { PYBIND11_OVERRIDE(std::string, Animal, name, ); }
};
template <class DogBase = Dog> class PyDog : public PyAnimal<DogBase> {
public:
    using PyAnimal<DogBase>::PyAnimal; // Inherit constructors
    // Override PyAnimal's pure virtual go() with a non-pure one:
    std::string go(int n_times) override { PYBIND11_OVERRIDE(std::string, Dog, go, n_times); }
    std::string bark() override { PYBIND11_OVERRIDE(std::string, Dog, bark, ); }
};

Now compilation succeeds.
Thanks.

Reproducible example code

No response

Is this a regression? Put the last known working version here if it is.

Not a regression

Start at the Inheritance section, “Combining virtual functions and inheritance,” linked in the issue. Compare the overloaded virtual-method example with the corrected version, update the documented override macros to use the appropriate base classes, and verify that the example compiles.