Are you using the stock messaging app?
I'm running the Samsung messages app. I opened the messages app settings menu and selected more settings. A new menu opens with items text messages and mms messages. I selected each one and both have the option for turning delivery reports on or off. You should have the same option available.
Galaxy S9 SM-G960U
Security Patch Level
December 1st , 2019
Delivery Reports are a feature that is provided by the service providers. Therefore, not everyone has access to this feature. Please contact your service provider to verify feature availability.