Mechanical Regimes in Gelatin and Gellan Gum Bigels: Structure–Function Relationships and Dual Delivery of Carob Fruit Extracts

Bigels (BGs) were formulated using gelatin (GA) or gellan gum (GG) hydrogels (HGs) combined with beeswax-structured oleogels (OGs). Carob fruit extracts—an inositol-rich fraction (I-CFE) and a polyphenol-rich fraction (P-CFE)—were incorporated into the HG and OG phases, respectively, to enable dual delivery. The effects of composition on rheological, textural, thermal, color, and stability properties were evaluated at HG/OG ratios of 70/30, 60/40, and 50/50. GG-based BGs formed rigid, coherent, and crystal-reinforced networks, exhibiting the highest oscillatory stiffness and complex viscosity. GA-based BGs developed softer, more deformable, and viscous structures, with mechanical behavior strongly governed by damping and water content. Increasing OG content reinforced GG BGs through beeswax–crystal integration, whereas in GA it increased oscillatory stiffness but weakened the cohesive, viscous, and recoverable characteristics of the protein network. Categorical principal component analysis (CATPCA) revealed two mechanical domains: a GA-associated regime dominated by viscosity, penetration resistance, and loss factor (tan δ), and a GG-associated regime governed by elastic stiffness. Correlations confirmed tan δmax as a marker of structural fragility in GA, while stiffness parameters dominated GG behavior. Melting points remained within 53–54 °C, and all BGs showed excellent physical stability. Overall, GA and GG provide complementary design spaces, offering a mechanistic basis for the rational design of BGs with controlled structural and functional properties.