Splitting my Macbook Pro desktop over 2 external monitors

You CAN use ONE external display and the built-in display together as one extended desktop, and freely move the mouse and drag windows across the line between the two displays.

But on your model MacBook Pro 13-in, the rasterizer/Display-Generator that runs the built-in display can NOT be re-purposed to run a second external display.

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.