Hello JorgeCas,
this answer, especially the second link, was very helpful.
Because I had already tried unsuccessfully to integrate the SDK into MCUxpresso but also into the MCUxpresso plugin for VSCode. But with the link, which contained more detailed instructions, it worked without any problems. Now I can use my Segger debug probe from an IDE in the same way as I used to do when debugging MCUs (like the LPC55S16). It was also an advantage that the description mentioned the installer included in the plugin. Because my previously manually installed toolchain, with which I could compile the example programs manually, did not work from the VSCode plugin. When I installed the compiler toolchain again using the installer (which I would never have found without the instructions), everything worked without any problems.
Many thanks for your help.