build(java): enable snippet-bot (#266)

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Synth log will be available here:
https://source.cloud.google.com/results/invocations/18040a8c-dd59-4849-a8e5-91f73765acf9/targets

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Source-Link: googleapis/synthtool@5a506ec

synth.metadata

@@ -4,7 +4,7 @@
       "git": {
         "name": ".",
         "remote": "https://github.com/googleapis/java-secretmanager.git",
-        "sha": "b98960888d43fcb5db55190876a1e77ebab2c7f7"
+        "sha": "46b9e3237642fbf3300ef53a64df287e8d696908"
       }
     },
     {
@@ -19,7 +19,7 @@
       "git": {
         "name": "synthtool",
         "remote": "https://github.com/googleapis/synthtool.git",
-        "sha": "7c5370937dd9ba9dcf9cd7d2af880a58b389b4f1"
+        "sha": "5a506ec8765cc04f7e29f888b8e9b257d9a7ae11"
       }
     }
   ],
@@ -51,6 +51,7 @@
     ".github/PULL_REQUEST_TEMPLATE.md",
     ".github/readme/synth.py",
     ".github/release-please.yml",
+    ".github/snippet-bot.yml",
     ".github/trusted-contribution.yml",
     ".github/workflows/approve-readme.yaml",
     ".github/workflows/auto-release.yaml",