Elemental and Isotopic Yields from T Coronae Borealis: Predictions and Uncertainties
T Coronae Borealis (T CrB) is a symbiotic recurrent nova system expected to undergo its next outburst within the next two years. Recent hydrodynamic simulations have predicted the nucleosynthetic yields for both carbon-oxygen (CO) and oxygen-neon (ONe) white-dwarf models, but without accounting for thermonuclear reaction-rate uncertainties. We perform detailed Monte Carlo post-processing nucleosynthesis calculations based on updated thermonuclear reaction rates and uncertainties from the 2025 evaluation. We quantify the resulting abundance uncertainties and identify the key nuclear reactions that dominate them. Our results show that both the CO and ONe nova models robustly produce characteristic CNO isotopes. More pronounced abundance differences emerge for elements with A $\ge$ 20. Sulfur is the most robust observational discriminator between the CO and ONe nova models, with a model-to-model difference of a factor of $\approx$30 and minimal sensitivity to reaction rate uncertainties. Neon, silicon, and phosphorus exhibit even larger abundance differences (factors of $\approx$150-250), providing strong diagnostic potential. While their predicted yields are subject to larger uncertainties, these remain smaller than the model-to-model differences, allowing these elements to serve as useful, though less precise, tracers of white-dwarf composition. Chlorine, argon, and potassium also differ between models, but the 1$\sigma$-abundance ranges for the CO and ONe models overlap, reducing their present usefulness as composition tracers. We find that only nine nuclear reactions dominate the abundance uncertainties of the most diagnostically important isotopes, and their influence is largely independent of the underlying white-dwarf composition. These results provide guidance for future experimental efforts and for interpreting ejecta compositions in the next eruption of T CrB.