Do not set response status in ServerHttpObservationFilter

Prior to this commit, the `ServerHttpObservationFilter` would set the
response status (and possibly overwrite it) in case an exception is
found as an attribute.
While the exception itself should be used in the observation, the filter
should have no side effect on the response.

Fixes gh-29353

spring-web/src/main/java/org/springframework/web/filter/ServerHttpObservationFilter.java

@@ -27,7 +27,6 @@ import jakarta.servlet.ServletException;
 import jakarta.servlet.http.HttpServletRequest;
 import jakarta.servlet.http.HttpServletResponse;
 
-import org.springframework.http.HttpStatus;
 import org.springframework.http.observation.DefaultServerRequestObservationConvention;
 import org.springframework.http.observation.ServerHttpObservationDocumentation;
 import org.springframework.http.observation.ServerRequestObservationContext;
@@ -117,7 +116,6 @@ public class ServerHttpObservationFilter extends OncePerRequestFilter {
 			if (!request.isAsyncStarted()) {
 				Throwable error = fetchException(request);
 				if (error != null) {
-					response.setStatus(HttpStatus.INTERNAL_SERVER_ERROR.value());
 					observation.error(error);
 				}
 				observation.stop();

spring-web/src/test/java/org/springframework/web/filter/ServerHttpObservationFilterTests.java

@@ -70,7 +70,7 @@ class ServerHttpObservationFilterTests {
 		ServerRequestObservationContext context = (ServerRequestObservationContext) this.request
 				.getAttribute(ServerHttpObservationFilter.CURRENT_OBSERVATION_CONTEXT_ATTRIBUTE);
 		assertThat(context.getError()).isEqualTo(customError);
-		assertThatHttpObservation().hasLowCardinalityKeyValue("outcome", "SERVER_ERROR");
+		assertThatHttpObservation().hasLowCardinalityKeyValue("exception", "IllegalArgumentException");
 	}
 
 	@Test