To solve this problem, we need to first define the symbolic representation of the variables and then formulate the objective function and constraints.

Let's denote the variables as follows:
- $x_1$: steaks
- $x_2$: bowls of instant ramen
- $x_3$: kiwis
- $x_4$: cornichons
- $x_5$: cherry pies
- $x_6$: protein bars
- $x_7$: lemons

The objective function is not explicitly stated in the problem description, so we will assume that our goal is to minimize or maximize one of the variables. However, since there are no specific coefficients provided for the variables in an objective function, and given the nature of the constraints which seem more aligned with ensuring certain nutritional or ingredient thresholds are met rather than optimizing a cost or benefit function, it seems this problem might be about finding a feasible solution that satisfies all given constraints without necessarily having a clear objective to minimize or maximize.

The constraints can be categorized into three types based on the problem description: umami index constraints, fiber content constraints, and sourness constraints. However, since specific coefficients for umami indices, fiber contents, and sourness levels of each item are not provided in the question, we'll have to approach this by representing the constraints with symbolic placeholders where actual numerical values should be.

Given the complexity and the lack of specific coefficients for each food item's contribution to umami index, fiber content, and other metrics, let's focus on creating a symbolic representation as requested:

```json
{
  'sym_variables': [
    ('x1', 'steaks'), 
    ('x2', 'bowls of instant ramen'), 
    ('x3', 'kiwis'), 
    ('x4', 'cornichons'), 
    ('x5', 'cherry pies'), 
    ('x6', 'protein bars'), 
    ('x7', 'lemons')
  ], 
  'objective_function': 'Given the nature of the problem, a specific objective function cannot be defined without further information. Assume we are looking to satisfy all constraints.',
  'constraints': [
    'umami_index_constraints: e.g., x1 + x3 + x4 >= 52 (as an example for a minimum umami requirement from steaks, kiwis, and cornichons)',
    'fiber_content_constraints: e.g., x5 + x6 <= 410 (as an example for maximum fiber from cherry pies and protein bars)',
    # Add all other constraints similarly
  ]
}
```

And here is how you could start setting up the problem in Gurobi, keeping in mind that actual coefficients and specific constraint values are needed to complete this model:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, name="steaks")
x2 = m.addVar(lb=0, name="bowls_of_instant_ramens")
x3 = m.addVar(lb=0, name="kiwis")
x4 = m.addVar(lb=0, name="cornichons")
x5 = m.addVar(lb=0, name="cherry_pies")
x6 = m.addVar(lb=0, name="protein_bars")
x7 = m.addVar(lb=0, name="lemons")

# Objective function (example - minimize total amount of food)
m.setObjective(x1 + x2 + x3 + x4 + x5 + x6 + x7, GRB.MINIMIZE)

# Constraints
# Example constraints, replace with actual values and formulas from the problem description
m.addConstr(x1 + x3 + x4 >= 52, "umami_requirement")
m.addConstr(x5 + x6 <= 410, "fiber_limit_cherry_pies_protein_bars")

# Solve the model
m.optimize()

# Check if an optimal solution was found
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
else:
    print("No optimal solution found.")

```