chore(librarian): sync post processing scripts (#14447)

Sync post processing scripts in
[.librarian/generator-input](https://github.com/googleapis/google-cloud-python/tree/main/.librarian/generator-input)
with
[scripts/client-post-processing](https://github.com/googleapis/google-cloud-python/tree/main/scripts/client-post-processing).

Author: parthea

.librarian/generator-input/client-post-processing/add-missing-dependencies-to-setup-py-constraints.yaml

@@ -161,3 +161,43 @@ replacements:
           "google-cloud-org-policy >= 1.0.0, <2.0.0",
           "proto-plus >= 1.22.3, <2.0.0",
     count: 1
+  - paths: [
+      packages/google-shopping-merchant-notifications/setup.py
+    ]
+    before: |
+      dependencies = \[
+          "google-api-core\[grpc\] >= 1.34.1, <3.0.0,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*,!=2.8.*,!=2.9.*,!=2.10.*",
+          # Exclude incompatible versions of `google-auth`
+          # See https://github.com/googleapis/google-cloud-python/issues/12364
+          "google-auth >= 2.14.1, <3.0.0,!=2.24.0,!=2.25.0",
+          "proto-plus >= 1.22.3, <2.0.0",
+          "proto-plus >= 1.25.0, <2.0.0; python_version >= '3.13'",
+          "protobuf>=3.20.2,<7.0.0,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5",
+      \]
+    after:  |
+      dependencies = [
+          "google-api-core[grpc] >= 1.34.1, <3.0.0,!=2.0.*,!=2.1.*,!=2.2.*,!=2.3.*,!=2.4.*,!=2.5.*,!=2.6.*,!=2.7.*,!=2.8.*,!=2.9.*,!=2.10.*",
+          # Exclude incompatible versions of `google-auth`
+          # See https://github.com/googleapis/google-cloud-python/issues/12364
+          "google-auth >= 2.14.1, <3.0.0,!=2.24.0,!=2.25.0",
+          "proto-plus >= 1.22.3, <2.0.0",
+          "proto-plus >= 1.25.0, <2.0.0; python_version >= '3.13'",
+          "protobuf>=3.20.2,<7.0.0,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5",
+          "google-shopping-type >= 1.0.0, <2.0.0",
+      ]
+    count: 1
+  - paths: [
+      packages/google-shopping-merchant-notifications/testing/constraints-3.7.txt
+    ]
+    before: |
+      google-api-core==1.34.1
+      google-auth==2.14.1
+      proto-plus==1.22.3
+      protobuf==3.20.2
+    after:  |
+      google-api-core==1.34.1
+      google-auth==2.14.1
+      proto-plus==1.22.3
+      google-shopping-type==1.0.0
+      protobuf==3.20.2
+    count: 1