To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify the constraints provided. The objective function aims to maximize `5.97 * eggs + 9.26 * hot_dogs`. The constraints can be summarized as follows:

1. Fiber constraint: `7 * eggs + 6 * hot_dogs <= 53` (since there's an upper bound of 53 grams of fiber).
2. Sourness index constraint: `1 * eggs + 9 * hot_dogs <= 25` (upper bound of sourness index is given as 25, but we also have a maximum total sourness index constraint of 21 which will override this).
3. Minimum fiber requirement: `7 * eggs + 6 * hot_dogs >= 12`.
4. Minimum sourness requirement: `1 * eggs + 9 * hot_dogs >= 4`.
5. Additional linear constraint: `-3 * eggs + 2 * hot_dogs >= 0`.
6. Maximum fiber constraint (repeated but will use the stricter one): Since we have two maximum fiber constraints, we'll consider the stricter or most limiting one which is `7 * eggs + 6 * hot_dogs <= 26` (as it's more restrictive than 53 grams when considering the need to maximize and not exceed).
7. Maximum sourness index constraint: `1 * eggs + 9 * hot_dogs <= 21`.

Given that both eggs and hot dogs can be non-integer values, we'll define them as continuous variables in Gurobi.

Here's how you could set up this problem in Python using Gurobi:

```python
from gurobipy import *

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

# Define the variables
eggs = m.addVar(vtype=GRB.CONTINUOUS, name="eggs")
hot_dogs = m.addVar(vtype=GRB.CONTINUOUS, name="hot_dogs")

# Set the objective function
m.setObjective(5.97 * eggs + 9.26 * hot_dogs, GRB.MAXIMIZE)

# Add constraints
m.addConstr(7 * eggs + 6 * hot_dogs >= 12, "min_fiber")
m.addConstr(1 * eggs + 9 * hot_dogs >= 4, "min_sourness")
m.addConstr(-3 * eggs + 2 * hot_dogs >= 0, "additional_constraint")
m.addConstr(7 * eggs + 6 * hot_dogs <= 26, "max_fiber")
m.addConstr(1 * eggs + 9 * hot_dogs <= 21, "max_sourness")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Eggs: {eggs.x}")
    print(f"Hot Dogs: {hot_dogs.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```