mixture separation

Generally extraction through reflux is used in line with a Soxhlet extractor, to justify the use of a soxhlet extractor is to know the solubility of your product versus possible impurities in a particular solvent. In this case, an aromatic ester will most likely be soluble in many organic solvents such as DCM or Ethyl Acetate. Extremely limited solubility will warrant the use of a Soxhlet extractor which refluxes the solvent to increase solubility.

Filtration is used, clearly, when your product is insoluble in a particular solvent. In this case, you have a two-phase mixture of an aqueous system (the acid, now neutralised by the base). So this isn't correct.

Recrystallisation is a purification process that could be used after extraction if your product is crystalline at room temperature, for this we ideally need a single phase solvent system - not a mixture of water and organic solvent. So this isn't correct.

Solvent extraction is probably one of the most common extraction processes used, it's the first stage of processing which is to remove many impurities that are soluble in water (and to remove water itself) and not soluble in organic solvents - or less commonly, vice versa.