Many moons ago, when I was deeply interested in traditional hand-powered woodworking, and wanted nothing to do with modern gadgets or electricity, I had made a "shop humidity gauge" out of a cross cut of a wide flatsawn board with one end screwed to a steel bar. The bar had markings for 30, 40, 50% etc at the points that matched the wood's dimension for the given humidity. It provided a good reference point for how much slack to leave in joinery for things like wide breadboard ends on a table top - which was very helpful, since the shop I used then was not climate controlled at all and would seasonally swing quite a bit.
You can look up the expansion rates for specific species on wood-database.com - it lists radial (quartersawn) and tangential (flatsawn) rates per species. 3% net change in moisture content in a climate controlled space sounds like a lot to me, but I guess it depends on what you mean by "climate controlled." This page has a graph at the bottom showing the moisture content your wood will have at equillibrium for a given temperature and humidity:
https://www.woodproducts.fi/content/moisture-properties-wood
Using that reference and the data on wood-finder you can figure exactly what the change will be.
Personally, I don't specifically look for flatsawn or quartersawn, but rather just the quality and appearance of the specific board. We want our instruments to be durable to humidity changes, but IME that comes just as much if not more from the design and construction than just the wood being sawn a certain way. For instance - radiusing a back or top gives it compliance where it can respond to dimensional changes safely (by pushing the curve bigger or smaller) instead of being forced to split itself apart, like a flat back can. When I started building, I purposefully jacked my shop to 70% humidity for a few days, then made a pair of test backs - one flat, one dished - and put them in front of a fan in my garage, where the humidity was around 20%. Surely enough, the flat back had split a few weeks later, and the dished back just deformed.