How to fix sagging plaster under window
There is a strong chance that what you see is drywall overlaid a plaster wall. Plaster, does not sag or bow out as it is shown in your picture, not without severe cracking. Plaster is very brittle and does not take well to any movement at all.

Based only on what the picture shows, the plaster did move, or cracked or fell off or something like that. The remedy that somebody thought of, which is done a lot, is overlay the wall with drywall, whether it be 1/4" thick or thicker.

Flat window trim in homes the age your is typically very thick, 3/4"-7/8" thick, unless it was redone with newer stock. Regardless, the trim's edge is covered to a degree by the wall material, suggesting an overlay of drywall over the plaster.

To answer your question, since the base is already off, so it appears, cut the offending section out to the original wall surface, remove whatever is creating the waves in the wall and re-shim if needed and reinstall the same thickness of new drywall that was removed. It will still cover the trim to a degree, but it will be uniform.