How do I clean/speed up my iPhone 13 Pro Max?

Force Restart your device:

• Quickly press and release volume up
• Quickly press and release volume down
• Press and hold the side button until the Apple logo appears. Ignore anything else you see on the screen while holding the button and it could take up to 15 seconds before seeing the Apple Logo.

No additional steps are needed for cleanup, but you will want to make sure you have adequate free space on your phone when viewing at Settings > General > iPhone Storage. When storage space runs low, you will see unexpected results.

If you recently updated the OS, there are background processes still running where you will see a slower than normal operation until those are completed. That could take a couple of days.

You can also check your battery at Settings > Battery > Battery Health & Charging. If the Maximum Capacity is below 80%, it is time for a replacement. You will also see a section called Peak Performance Capability, and it should show normal. Performance may be limited to prevent unexpected shutdowns when the battery has not been able to provide enough power.

iPhone battery and performance - Apple Support