Novel Ionic Liquid for the Liquid–Liquid Microextraction of Allura Red (AR, E129) from Food Samples: A Box–Behnken Optimization Approach

3-[(2S)-2-Hydroxy-3-phenoxypropyl]-1-methyl-1H-imidazol-3-ium hexafluorophosphate (IL-2) has been synthesized for the liquid–liquid microextraction of Allura Red (AR) from industrial food products. The novel ionic liquid has been characterized using 1H NMR,13C NMR,31P NMR, and FT-IR spectroscopy. The extraction procedure was optimized by investigating the effects of pH, ionic liquid volume, ultrasonication time, and centrifugation time through a Box–Behnken experimental design. The significance and interactions of the experimental variables were evaluated using response surface methodology. Under the optimized conditions, the proposed method was validated in terms of its analytical performance. The obtained limit of detection (LOD), preconcentration factor, and enhancement factor were 2.65, 42.9, and 54.8, respectively. The developed procedure was employed to the determination of E129 in industrial food products. The AGREE score of the proposed method was calculated as 0.70, indicating a satisfactory level of environmental sustainability.