Why are they so sharp? I've tried typing T and making it a Bezier but the only one handle appears
Here's an example similar to yours:
On Frame 1, I set a location Keyframe. On Frame 10, I moved the camera up on the Z axis and set another location Keyframe. I'm only showing the Z curve.
Notice that I've manually rotated the handles for the Keyframe at frame 10 but that has no effect on the curve to the right of the keyframe. Intuitively, that's because the camera has stopped moving.
Now I've moved to frame 15, moved the camera down, and added a keyframe. I've also rotated the handles for that keyframe:
Now there's a smooth transition at frame 10, but a sharp one at frame 15.
The F Curve for location always shows the curve after the last keyframe as a flat line, because you've stopped moving the camera.