Macbook pro m2 not detected second monitor after update to os 13

Apple-Silicon 2020 M1 13-in MacBook Pro and Air and 2022 Apple-Silicon M2 13-in MacBook Pro and Air are extremely-capable entry-level computers. They can support the internal display AND an External display up to the previously unheard of size of the Apple 6K display at billions of colors. But only ONE in addition to the internal display.

This may not match the way older computers forced you to work, since older computers were not able to support a really large external display. But it is NOT a defect. The spec was available long before you could purchase the computer.

The Apple standard for its built-in hardware-accelerated displays, makes them suitable for full-motion video for production/display of cinema-quality video with NO dropped frames, and NO dropouts or partial-blank scan lines due to memory under-runs or other issues. This requires a hardware rasterizer/display-generator for each fully-accelerated display. 

DisplayLink technology creates a "fake" display buffer in RAM, sends the data out over a slower interface to a stunt box with DisplayLink custom chips that put that data back onto a "legacy" interface.  It is not a true "accelerated" display, and it can suffer from lagging. Just adding the DisplayLink Driver is not adequate to get a picture -- you need a DisplayLink "stunt-box" or a Dock that includes DisplayLink chips.

If you did a software update and lost your second external display, it could mean you need an updated version of DisplayLink software.