The shower diverter in our spare bathroom doesn’t really work. The faucet is also gross and I want to change it.

I took the faucet off the wall and the pipe doesn’t match what I’m seeing in videos. My faucet doesn’t quite match the ones at Home Depot.

Most instructions I’m seeing show the pipe coming out of the wall:

My pipe is recessed in the wall:

My faucet has a piece of pipe extending out of it:

All the faucets I see in stores or online don’t have any pipe on them. They’re expecting the pipe to be sticking out of the wall.

Do I need to find a piece of pipe to make an adapter? Or is there a type of faucet I should be looking at that has this connection?