Lockdown Mode and picture messages.

After turning Lockdown Mode off try a Forced Restart:

Force restart iPhone - Apple Support

How Lockdown Mode protects your device

When Lockdown Mode is enabled, some apps and features will function differently, including:

• Messages - Most message attachment types are blocked, other than certain images, video, and audio. Some features, such as links and link previews, are unavailable. 
• Web browsing - Certain complex web technologies are blocked, which might cause some websites to load more slowly or not operate correctly. In addition, web fonts might not be displayed, and images might be replaced with a missing image icon.
• FaceTime - Incoming FaceTime calls are blocked unless you have previously called that person or contact.
• Apple services - Incoming invitations for Apple services, such as invitations to manage a home in the Home app, are blocked unless you have previously invited that person.
• Shared Albums - Shared albums are removed from the Photos app, and new Shared Album invitations are blocked. You can still view these shared albums on other devices that don’t have Lockdown Mode enabled. When you turn off Lockdown Mode, you need to turn Shared Albums on again in your device settings.
• Device connections - To connect your iPhone or iPad to an accessory or another computer, the device needs to be unlocked. To connect your Mac laptop with Apple silicon to an accessory, your Mac needs to be unlocked and explicit approval provided.
• Configuration profiles - Configuration profiles can’t be installed, and the device can’t be enrolled in Mobile Device Management or device supervision while in Lockdown Mode.

Phone calls and plain text messages continue to work while Lockdown Mode is enabled. Emergency features, such as SOS emergency calls, are not affected. 

Since that did not work about your only option is to Restore the iPhone, preferably as new (a pain I know) or from a backup.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support