Step 1: Understanding the Concept:
Total Soluble Solids (TSS) represents the percentage of dissolved solids (principally sugars, along with organic acids and soluble minerals) in fruit pulp, measured in degrees Brix ($^\circ\text{Brix}$).
Step 2: Detailed Explanation:
Let us compare the average ripe-stage TSS of the given fruits:
1. Bael (Aegle marmelos): This hardy, arid-zone fruit contains exceptionally dense, sweet pulp rich in mucilage, pectins, and sugars. Its TSS regularly ranges from $30^\circ\text{Brix}$ to $40^\circ\text{Brix}$.
2. Mango (Mangifera indica): Ripe fruits typically range from $15^\circ\text{Brix}$ to $20^\circ\text{Brix}$.
3. Grapes (Vitis vinifera): Usually range between $16^\circ\text{Brix}$ and $24^\circ\text{Brix}$ depending on the cultivar.
4. Sapota (Manilkara zapota): Shows a high sugar level, typically ranging from $20^\circ\text{Brix}$ to $24^\circ\text{Brix}$.
Bael clearly has the highest sugar density and total soluble solids among the options provided.
Step 3: Final Answer:
Bael has the highest TSS of up to $40^\circ\text{Brix}$.