What’s the best way to repair a cracked and chipped corner?

While I haven't done the exact repair you're dealing with, I suggest taking off the drain section for better access. Use plywood to make a straight edge on one side for a clean corner. Then, apply some foundation or concrete fill. After it cures, shift the board to the other side and repeat. This approach should help you achieve a nice square corner. Just remember to match the color when you finish, or you might need to paint the whole area later.

To fix a cracked corner like yours, you should use a product called "mortar-all," which is available at Home Depot. It's a stiff, quick-setting mortar that's easy to shape. Just avoid the "latex repair patch"—it's not great. You'll also need a flat or pointed trowel (I recommend a tile edge trowel for this work), a quart-size mixing container, and a sponge. Start by cleaning the area and removing any loose material. Mix the mortar with water until it’s stiff but moldable, then apply it quickly to the wall using the trowel. Finish by smoothing it out with the sponge so it blends with the surrounding area.