Context. Space-based mid-infrared (IR) spectroscopy is a powerful tool for the characterization of important star formation tracers of warm gas which are unobservable from the ground. The previous mid-IR spectra of bright high-mass protostars with the Infrared Space Observatory (ISO) in the hot-core phase typically show strong absorption features from molecules such as CO₂, C₂H₂, and HCN. However, little is known about their fainter counterparts at earlier stages. Aims. We aim to characterize the gas-phase molecular features in James Webb Space Telescope Mid-Infrared Instrument Medium Resolution Spectrometer (MIRI/MRS) spectra of the young and clustered high-mass star-forming region IRAS 23385+6053. Methods. Spectra were extracted from several locations in the MIRI/MRS field of view, targeting two mid-IR sources tracing embedded massive protostars as well as three H₂ bright outflow knots at distances of >8000 au from the multiple. Molecular features in the spectra were fit with local thermodynamic equilibrium (LTE) slab models, with their caveats discussed in detail. Results. Rich molecular spectra with emission from CO, H₂, HD, H₂O, C₂H₂, HCN, CO₂, and OH are detected towards the two mid-IR sources. However, only CO and OH are seen towards the brightest H₂ knot positions, suggesting that the majority of the observed species are associated with disks or hot core regions rather than outflows or shocks. The LTE model fits to ¹²CO₂, C₂H₂, HCN emission suggest warm 120–200 K emission arising from a disk surface around one or both protostars. The abundances of CO₂ and C₂H₂ of ~10⁻⁷ are consistent with previous observations of high-mass protostars. Weak ~500 K H₂O emission at ~6–7 µm is detected towards one mid-IR source, whereas 250–1050 K H₂O absorption is found in the other. The H₂O absorption may occur in the disk atmosphere due to strong accretion-heating of the midplane, or in a disk wind viewed at an ideal angle for absorption. CO emission may originate in the hot inner disk or outflow shocks, but NIRSpec data covering the 4.6 µm band head are required to determine the physical conditions of the CO gas, as the high temperatures seen in the MIRI data may be due to optical depth. OH emission is detected towards both mid-IR source positions and one of the shocks, and is likely excited by water photodissociation or chemical formation pumping in a highly non-LTE manner. Conclusions. The observed molecular spectra are consistent with disks having already formed around two protostars in the young IRAS 23385+6054 system. Molecular features mostly appear in emission from a variety of species, in contrast to the more evolved hot core phase protostars which typically show only absorption; however, further observations of young high-mass protostars are needed to disentangle geometry and viewing angle effects from evolution.