Document how to mark an observation as an error

The `ServerHttpObservationFilter` implementations record observations
for processed HTTP exchanges. The `Observation.Context` contains various
metadata contributed by the observation convention. The instrumentation
can also mark the observation as an error by setting any `Throwable` on
the context.

Because the instrumentation is done as filters, only exceptions reaching
the filter can be considered. Any error handled at a lower level by the
Framework can, or cannot be considered as an error for an observation.

This commit documents how a web application should opt-in for
considering a handled exception as an error for the current observation.

Closes gh-29848

framework-docs/src/main/java/org/springframework/docs/integration/observability/httpserver/reactive/UserController.java

@@ -0,0 +1,42 @@
+/*
+ * Copyright 2002-2023 the original author or authors.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      https://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.springframework.docs.integration.observability.httpserver.reactive;
+
+import org.springframework.http.ResponseEntity;
+import org.springframework.stereotype.Controller;
+import org.springframework.web.bind.annotation.ExceptionHandler;
+import org.springframework.web.filter.reactive.ServerHttpObservationFilter;
+import org.springframework.web.server.ServerWebExchange;
+
+@Controller
+public class UserController {
+
+	@ExceptionHandler(MissingUserException.class)
+	ResponseEntity<Void> handleMissingUser(ServerWebExchange exchange, MissingUserException exception) {
+		// We want to record this exception with the observation
+		ServerHttpObservationFilter.findObservationContext(exchange)
+				.ifPresent(context -> context.setError(exception));
+		return ResponseEntity.notFound().build();
+	}
+
+	// @fold:on
+	static class MissingUserException extends RuntimeException {
+
+	}
+	// @fold:off
+
+}

framework-docs/src/main/java/org/springframework/docs/integration/observability/httpserver/servlet/UserController.java

@@ -0,0 +1,43 @@
+/*
+ * Copyright 2002-2023 the original author or authors.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      https://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.springframework.docs.integration.observability.httpserver.servlet;
+
+import jakarta.servlet.http.HttpServletRequest;
+
+import org.springframework.http.ResponseEntity;
+import org.springframework.stereotype.Controller;
+import org.springframework.web.bind.annotation.ExceptionHandler;
+import org.springframework.web.filter.ServerHttpObservationFilter;
+
+@Controller
+public class UserController {
+
+	@ExceptionHandler(MissingUserException.class)
+	ResponseEntity<Void> handleMissingUser(HttpServletRequest request, MissingUserException exception) {
+		// We want to record this exception with the observation
+		ServerHttpObservationFilter.findObservationContext(request)
+				.ifPresent(context -> context.setError(exception));
+		return ResponseEntity.notFound().build();
+	}
+
+	// @fold:on
+	static class MissingUserException extends RuntimeException {
+
+	}
+	// @fold:off
+
+}