Serval folks around here are nope to stoves under windows- cleaning issues and such. You big issue is an obvious one- how to handle ventilation? You would need to figure that one out.

Any particular reason why you are thinking of moving your plumbing and putting a stove there instead?

Is setting fire to your window trim and breaking the glass a good enough reason? You’d have to rebuild the wall with new windows and a whole bunch more expensive requirements.

When we moved in to our current house, the electric glass cooktop was under a window. It had a downdraft vent that was pretty much useless and grease would always get on the window.

We remodeled and put the sink under that window and moved the cooktop to a side wall where we could install a real vent hood.

It's also more pleasant to gaze out a window while washing up rather then when stirring something on the stove. Generally people spend more time prepping and washing, than actively cooking/stirring etc at the stove.

So, I should have mentioned that the stove is ALREADY under a window and has no ventilation. This is a 1940s summer cottage and not exactly up to code (in many respects!). Trying to figure out how to improve the layout of the kitchen. The side that currently has the stove is a much better view out into the yard (vs. the garage/parking pad outside the left window), so we'd rather have the sink on that side. No obvious way to arrange this kitchen for the better ... I welcome any ideas!

where the sink is currently

Yes, which would fall between the windows. Many Houzzers have inspiration pics of just that:

Looks like you may need to reduce the width of the window sizes, and the exhaust can just go straight out the wall.

If we move the stove to where that large built-in cabinet currently is, it will impinge a bit on the space for the table ...