feat: Update synth.py to copy discovery files from discovery-artifact-manager (#1104)

Update synth.py to copy discovery files from discovery-artifact-manager

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- [x] Make sure to open an issue as a [bug/issue](https://github.com/googleapis/google-api-python-client/issues/new/choose) before writing your code!  That way we can discuss the change, evaluate designs, and agree on the general idea
- [x] Ensure the tests and linter pass
- [x] Code coverage does not decrease (if any source code was changed)
- [x] Appropriate docs were updated (if necessary)

Closes #1103 🦕
diff --git a/synth.py b/synth.py
index e68036b..5799074 100644
--- a/synth.py
+++ b/synth.py
@@ -14,6 +14,9 @@
 
 import synthtool as s
 from synthtool import gcp
+from synthtool.sources import git
+
+DISCOVERY_ARTIFACT_MANAGER_REPO = "googleapis/discovery-artifact-manager"
 
 common = gcp.CommonTemplates()
 
@@ -29,4 +32,20 @@
 # Also move issue templates
 s.move(templated_files / '.github')
 
-s.shell.run(["nox", "-s", "docs"], hide_output=False)
\ No newline at end of file
+# ----------------------------------------------------------------------------
+# Copy discoveries folder from discovery-artifact-manager repo
+# ----------------------------------------------------------------------------
+
+discovery_artifact_manager_url = git.make_repo_clone_url(DISCOVERY_ARTIFACT_MANAGER_REPO)
+discovery_artifacts = git.clone(discovery_artifact_manager_url) / "discoveries"
+
+excludes = [
+    "**/BUILD.bazel",
+]
+s.copy(discovery_artifacts,
+       "googleapiclient/discovery_cache/documents", excludes=excludes)
+
+# ----------------------------------------------------------------------------
+# Generate docs
+# ----------------------------------------------------------------------------
+s.shell.run(["nox", "-s", "docs"], hide_output=False)