sr/sharded_store: verbose messages on post schema

When an incompatible schema is posted, include the verbose compatibility
messages in the error message.

This helps users understand the reason for the incompatibility and it
matches the reference implementation.

Includes a minor fix to the way the compatibility level message is
formatted.

src/v/pandaproxy/schema_registry/sharded_store.cc

@@ -201,14 +201,15 @@ sharded_store::get_schema_version(subject_schema schema) {
     // Check compatibility of the schema
     if (!v_id.has_value() && !versions.empty()) {
         auto compat = co_await is_compatible(
-          versions.back().version, schema.schema.share());
-        if (!compat) {
+          versions.back().version, schema.schema.share(), verbose::yes);
+        if (!compat.is_compat) {
             throw exception(
               error_code::schema_incompatible,
               fmt::format(
                 "Schema being registered is incompatible with an earlier "
-                "schema for subject \"{}\"",
-                sub));
+                "schema for subject \"{}\", details: [{}]",
+                sub,
+                fmt::join(compat.messages, ", ")));
         }
     }
     co_return has_schema_result{s_id, v_id};
@@ -826,7 +827,7 @@ ss::future<compatibility_result> sharded_store::do_is_compatible(
             version_messages.emplace_back(
               fmt::format("{{oldSchema: '{}'}}", to_string(old_valid.raw())));
             version_messages.emplace_back(
-              fmt::format("{{compatibility: {}}}", compat));
+              fmt::format("{{compatibility: '{}'}}", compat));
         }
 
         result.messages.reserve(

tests/rptest/tests/schema_registry_test.py

@@ -1588,6 +1588,17 @@ def test_compatibility_messages(self, schemas):
                 message in m for m in msgs
             ), f"Expected to find an instance of '{message}', got {msgs}"
 
+        self.logger.debug(
+            "Check post incompatible schema error message (expect verbose messages)"
+        )
+        result_raw = self._post_subjects_subject_versions(
+            subject=f"{topic}-key", data=incompatible_data)
+
+        assert result_raw.status_code == 409
+        msg = result_raw.json()["message"]
+        for message in ["oldSchemaVersion", "oldSchema", "compatibility"]:
+            assert message in msg, f"Expected to find an instance of '{message}', got {msgs}"
+
     @cluster(num_nodes=3)
     def test_delete_subject(self):
         """