We present mid-infrared (MIR) spectral-timing measurements of the prototypical Galactic microquasar GRS 1915+105. The source was observed with the Mid-Infrared Instrument (MIRI) onboard JWST in June 2023 at an MIR luminosity $L_{\rm MIR}$ $\approx$ 10$^{36}$ erg s$^{-1}$ exceeding past infrared levels by about a factor of 10. In contrast, the X-ray flux is much fainter than the historical average, in the source's now-persistent 'obscured' state. The MIRI low-resolution spectrum shows a plethora of emission lines, the strongest of which are consistent with recombination in the hydrogen Pfund (Pf) series and higher. Low-amplitude ($\sim$1 per cent) but highly significant peak-to-peak photometric variability is found on time-scales of $\sim$1000 s. The brightest Pf (6-5) emission line lags the continuum. Though difficult to constrain accurately, this lag is commensurate with light-travel time-scales across the outer accretion disc or with expected recombination time-scales inferred from emission-line diagnostics. Using the emission line as a bolometric indicator suggests a moderate ($\sim$5-30 per cent Eddington) intrinsic accretion rate. Multiwavelength monitoring shows that JWST caught the source close in time to unprecedentedly bright MIR and radio long-term flaring. Assuming a thermal bremsstrahlung origin for the MIRI continuum suggests an unsustainably high mass-loss rate during this time unless the wind remains bound, though other possible origins cannot be ruled out. Polycyclic aromatic hydrocarbon features previously detected with Spitzer are now less clear in the MIRI data, arguing for possible destruction of dust in the interim. These results provide a preview of new parameter space for exploring MIR spectral timing in X-ray binaries and other variable cosmic sources on rapid time-scales.