samples: net: socketpair: clean up sample app

* use `read()` instead of `recv()`
* use `write()` instead of `send()`
* use `CONFIG_POSIX_API` and drop `<zephyr/posix/..>` prefix
* use `perror()`
* fix `Makefile.posix` to use `CC` instead of `CXX`
* fix race condition which caused an unhandled EOF
  and infinite loop, by adding a readback / echo
* Updated the docs to reflect the expected stdout
* Improve doc clarity

Signed-off-by: Chris Friedt <cfriedt@meta.com>