If the phone still vibrates and makes sounds but the screen randomly goes black, and it only comes back after disconnecting the battery, that usually points to a board-level issue rather than the display itself, especially since you already tried another screen.
On the iPhone 11 Pro this can be caused by a failing display power line, a short around the backlight circuit, or a power management issue triggered after the repair. It can also happen if there’s slight damage near the display connector or a component was disturbed during the battery or speaker replacement.
If it turns on long enough, check Settings > Privacy & Security > Analytics & Improvements > Analytics Data and look for panic-full logs. You can upload those to an online panic log analysis tool to see if there are display power or PMIC-related crashes happening before the screen cuts out.
Since swapping the LCD didn’t fix it, this is likely a logic board fault that needs microsoldering repair rather than another parts replacement.