pw_build: pw_python_package use public_deps for other_deps

This is already done for generated pw_python_packages but
non-generated ones were keeping it private.

Change-Id: Ie63df269e76a9747da0eb957b38084fe553490e9
Reviewed-on: https://pigweed-review.googlesource.com/c/pigweed/pigweed/+/128550
Pigweed-Auto-Submit: Anthony DiGirolamo <tonymd@google.com>
Reviewed-by: Alexei Frolov <frolv@google.com>
Commit-Queue: Auto-Submit <auto-submit@pigweed.google.com.iam.gserviceaccount.com>
diff --git a/pw_build/python.gni b/pw_build/python.gni
index 8e54086..cf74487 100644
--- a/pw_build/python.gni
+++ b/pw_build/python.gni
@@ -517,7 +517,7 @@
           inputs += invoker.inputs
         }
 
-        deps = _python_deps + _other_deps
+        public_deps = _python_deps + _other_deps
       }
     }