Soybean protein isolate (SPI) hydrogels are often ineffective as probiotic delivery vehicles during gastrointestinal (GI) digestion due to their limited structural stability. This study first examined whether tragacanth gum (TG, 10–20 g/L) and bitter almond gum (BAG, 10 g/L) could improve the structural and functional properties of SPI hydrogels. The selected SPI/TG hydrogel was then supplemented with ultrasound (US)-treated BAG, water-soluble BAG (SBAG), or fructooligosaccharide (10 g/L) and evaluated as a carrier for Lactobacillus rhamnosus GG (LGG) during simulated GI digestion and cold storage. Increasing TG concentration increased particle size from 853 to 1272 nm and reduced the absolute zeta potential from −31.44 to −27.52 mV. These changes indicate enhanced protein–polysaccharide interactions, as confirmed by FT-IR and fluorescence spectroscopy. TG also significantly improved water-holding capacity, swelling behavior, freeze–thaw stability, and rheological and textural parameters, reflecting improved network integrity. Hydrogels containing BAG and SBAG maintained LGG above 6 log CFU/g under simulated digestion. During cold storage, SBAG and US-treated BAG preserved probiotic viability more effectively than BAG, with LGG levels exceeding 7.5 log CFU/g. Overall, this study demonstrates that TG, BAG, and BAG derivatives can improve the performance of SPI-based hydrogels in protecting probiotics during processing, cold storage, and digestion.