How do I get privacy with my front door beautifully?

You can purchase privacy film from Home Depot and cut to your sizing.

Contact paper! Comes in all types of transparent patterns.

I would look at the big box stores for window film...most of these go on with water and come off with water (they also carry a "solution" that you can use). These would be better than contact paper because they have no glue. But leave at least 1 of two panes where the dog can look out!

I have a similar door and went to Lowes and got the window film with a slight decoration on it , like etched glass , but you can tell who is at the door without the person really seeing in. It works great winter and summer. My door gets REALLY hot in the summer and I haven't had any problems in 3 years.

Amazon has beautiful print films with motifs such as a design from a Klimt. These are very affordable and look like you have stained glass.

You can replace the glass with one that matches your stile. Based on the comments, you have a typical 18 Light insert in a steel or fiberglass door. I'm guessing it is an 8 foot door and the frame size holding the glass in place is 24" x 82" or 22" x 82", which are standard sizes. The clear glass is held in place with a frame. The attached image has a 12 light insert(24 x 50") that was changed out to a decorative glass insert. You can purchase one for your 18 light insert as well.

Privacy film. You can see out but no one can see in.