Missing 'Always On Display' option on iPhone 16 Pro

Are you sure you have an iPhone 16 Pro? Your tag line suggests you have an iPhone 16 Plus and if that is indeed the phone you have, it does have an Always On Display.

Open Settings > General > About > Model Name and report what it says.

If it’s not at Settings > Display & Brightness …

… check Settings > General > About > Model Name and report the results here.

According to Apple’s comparison tool, the iPhone 16 Plus does not have an Always-On display.