(Adams & Laughlin 1997) discuss the effect of increasing metallicity in the future. A higher metallicity increases the stellar burn rate since the density increases but
the higher opacity reduces it a bit. The total effect is nonlinear; in their model the maximal lifespan happens for $Z\approx 0.04$ and beyond that it declines. Whether there are newer and better models of this I do not know.
They also point out that the maximum stable stellar mass decreases as metallicity increases, while the mass of the minimum mass mainsequence star declines, both as a result of opacity effects.
Overall, the metallicity growth is likely to continue across the stelliferous era. While extragalactic gas may fall in, it merely adds to the hydrogen pool and continued star formation. What could stop the metallicity growth is quenching due to a galactic merger or active galactic nucleus that blows away enough gas to stop further star formation.