To solve the given optimization problem, we'll first define the variables and the objective function. Then, we'll formulate the constraints based on the provided conditions.

Let's denote:
- \(x_0\) as the number of knishes,
- \(x_1\) as the quantity of apples,
- \(x_2\) as the quantity of chicken drumsticks.

The objective function to minimize is given by:
\[8.01(x_0)^2 + 9.79(x_0)(x_1) + 4.17(x_1)(x_2) + 4.92(x_1) + 2.03(x_2)\]

Constraints:
1. Healthiness rating of knishes: \(26x_0\)
2. Healthiness rating of apples: \(3x_1\)
3. Healthiness rating of chicken drumsticks: \(19x_2\)
4. Combined healthiness rating from apples and chicken drumsticks should be at least 46: \(3x_1 + 19x_2 \geq 46\)
5. Total combined healthiness rating from all items should be at least 46: \(26x_0 + 3x_1 + 19x_2 \geq 46\)
6. The expression \(-4x_0 + 5x_2 \geq 0\)

Given the problem allows for non-integer quantities of all items, we can model this as a continuous optimization problem.

Here's how we could implement this in Gurobi using Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(name="knishes", lb=0)  # Number of knishes
x1 = m.addVar(name="apples", lb=0)   # Quantity of apples
x2 = m.addVar(name="chicken_drumsticks", lb=0)  # Quantity of chicken drumsticks

# Objective function
m.setObjective(8.01*x0**2 + 9.79*x0*x1 + 4.17*x1*x2 + 4.92*x1 + 2.03*x2, GRB.MINIMIZE)

# Constraints
m.addConstr(3*x1 + 19*x2 >= 46, name="apples_and_chicken_healthiness")
m.addConstr(26*x0 + 3*x1 + 19*x2 >= 46, name="total_healthiness")
m.addConstr(-4*x0 + 5*x2 >= 0, name="knishes_and_chicken_relation")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Knishes: {x0.x}")
    print(f"Apples: {x1.x}")
    print(f"Chicken Drumsticks: {x2.x}")
else:
    print("No optimal solution found.")
```

This code formulates the problem as described and attempts to find an optimal solution using Gurobi's solver. The variables `x0`, `x1`, and `x2` represent the quantities of knishes, apples, and chicken drumsticks, respectively. The objective function is defined according to the given formula, and constraints are added based on the healthiness ratings and the additional relationship between knishes and chicken drumsticks.