We present a JWST MIRI/MRS spectrum of the inner disk of WISE J044634.16–262756.1B (hereafter J0446B), an old (∼34 Myr) M4.5 star but with hints of ongoing accretion. The spectrum is molecule-rich and dominated by hydrocarbons. We detect 14 molecular species (H2, CH3, CH4, C2H2, 13CCH2, C2H4, C2H6, C3H4, C4H2, C6H6, HCN, HC3N, CO2, and 13CO2) and two atomic lines ([Ne ii] and [Ar ii]), all observed for the first time in a disk at this age. The detection of spatially unresolved H2 and Ne gas strongly supports that J0446B hosts a long-lived primordial disk, rather than a debris disk. The marginal H2O detection and the high C2H2/CO2 column density ratio indicate that the inner disk of J0446B has a very carbon-rich chemistry, with a gas-phase C/O ratio ≳2, consistent with what has been found in most primordial disks around similarly low-mass stars. In the absence of significant outer disk dust substructures, inner disks are expected to first become water-rich due to the rapid inward drift of icy pebbles and evolve into carbon-rich as outer disk gas flows inward on longer timescales. The faint millimeter emission in such low-mass star disks implies that they may have depleted their outer icy pebble reservoir early and already passed the water-rich phase. Models with pebble drift and volatile transport suggest that maintaining a carbon-rich chemistry for tens of Myr likely requires a slowly evolving disk with α-viscosity ≲10−4. This study represents the first detailed characterization of disk gas at ∼30 Myr, strongly motivating further studies into the final stages of disk evolution.