iPhone 15 Pro Do Not Disturb Mode Issue: Calls Rejected Instead of Silenced Notifications

I just switched to the iPhone 15 Pro from Android and I'm trying to get the Do Not Disturb (DND) mode working the way I'm used to. On my old Android phone, DND would silence notification sounds, but I could still see them on the screen if my phone was unlocked (with an option to toggle that on or off).

Here's my issue:

1. With DND turned on on my iPhone 15 Pro, my phone isn't just silencing calls, it seems to be rejecting them entirely.
2. When someone calls, they get a message that I'm busy or that I cut the call (on the caller's end).

Is this the normal behavior for Do Not Disturb on iPhone? Did I mess up a setting somewhere? I'm hoping to achieve the same functionality I had on Android, where calls are silenced but not directly rejecting them entirely.