Pretty, I'd rescue that too!
Over winter, might need some direct light to stay looking good. In a windowsill like that should be great. During summer, that can be a bit much, depending on location/latitude, time of day, heat.
Rex are rhizomatous type. The rhizomes store moisture, and can rot easily if there's not tons of oxygen, as you've seen, should do fabulously in the gritty. Water when dry, don't let plant get wilty. There's so much written about Rexes and rhizomatous Begs in general, you should be able to find enough reading material to keep you busy for weeks.
