To me, the only three things a camera needs to have if you want to seriously pursue photography are:
- Full Manual mode.
- RAW capability.
- A flash hotshoe.
You don't have to go dSLR/mirrorless to get these three functions; but they do tend to weed out the casual snapshot-cameras from the enthusiast models.
You want the PSAM modes and full Manual in particular, so that you can take explicit control over iso, aperture, and shutter speed for exposure.
You want RAW capability so that you can have the most latitude for post-processing vs. JPEG files that have lost data in the compression.
The flash hotshoe is more optional, but it makes learning to light with flash and off-camera flash much much easier and if someone wants to shoot portrait or product/still-life/food, can become key to image making.
For someone interested in shooting indoor sports, like gymnastics, they may require a fast telephoto lens, which might cost more than $100 on the lens alone; and is most likely to be fulfilled with an interchangeable-lens camera system.
To reach your price point, you're liable to have to go used market and older, discontinued gear. And we're talking gear that's at least a decade old, if not older if you have to purchase a body+a lens.
Arguably, she might actually do better with serious application to phone photography, where your $100 could subsidize getting a tripod adapter/tripod, more advanced camera apps, or books/classes on photography. If she's not allowed a phone then a used iPodTouch or small tablet might make more sense than a dedicated camera.