We numerically solve the conjectured quantum spectral curve for strings on AdS₃×S³×T⁴ with Ramond-Ramond charge from weak to strong coupling. At strong coupling, the spectrum organizes into flat-space string mass levels with universal square-root scaling in the string tension at leading order, and additional Kaluza-Klein fine-splitting at subleading order. At weak coupling, the energies are determined by a nearest-neighbor Bethe Ansatz, with universal subleading corrections that are suppressed at large volume.