Did you indent these or not? Multi-line arguments must be indented with at least 3 spaces.
debug_server =
/usr/local/bin/JLinkGDBServerCL
-device Cortex-M0
-speed auto
-if SWD
Also, check that the GDB server is opened at the expected port (I think localhost:3333). Check the output of /usr/local/bin/JLinkGDBServerCL -device Cortex-M0 -speed auto -if SWD manually to check that and adapt debug_port accordingly.
Also check that you are not running the latest extension version because there are issues with that: Cannot debug STM32: "Failed to launch GDB: Error: write EPIPE" - #7 by maxgerhardt