What DSLR exercises will help me learn manual control and see where it beats an iPhone for architecture or city photos?

A good way to learn is to run simple comparison exercises and review the results yourself.

Try the same scene with:

• different shutter speeds, from very fast to slow (for example 1/1000s to 1s)
• different apertures, from wide open to stopped down (for example f/1.8 to f/22)
• the same wide aperture at different subject distances, then repeat at f/2, f/2.8, f/4, etc.

This will teach you the exposure triangle and show how shutter speed affects motion, aperture affects depth of field, and focus distance changes the look of the image.

For architecture and landscapes, don’t expect a dramatic difference over a phone in every case, especially for small-screen viewing. Those subjects are often focused far away, so shallow depth of field matters less. Where the DSLR tends to help more is:

• difficult lighting, especially recovering shadow detail
• higher image quality when viewed large or cropped closely
• using a large aperture for selective focus
• using lenses with different focal lengths, especially wider or longer than a phone can manage optically

Also, spend some time reading about the exposure triangle, then repeat these tests in real scenes.