Include ConnectTimeoutException in timeout exceptions for rules

Motivation:

`CircuitBreakerRuleBuilder.onTimeException()` and
`RetryRuleBuilder.onTimeoutException()` only handle Armeria's
`com.linecorp.armeria.common.TimeoutException`. Howerver, they do not
treat Netty`s `ConnectTimeoutException` as a timeout.

Modifitions:

- Treat Netty's `ConnectTimeoutException` and
  `ProxyConnectException("timeout")` as a timeout for rules.

Result:

`CircuitBreakerRuleBuilder.onTimeException()` and `RetryRuleBuilder.onTimeoutException()`
now work when a connection or proxy establishment is timed out.

core/src/main/java/com/linecorp/armeria/client/AbstractRuleBuilder.java

@@ -42,6 +42,7 @@
 import com.linecorp.armeria.common.TimeoutException;
 import com.linecorp.armeria.common.annotation.Nullable;
 import com.linecorp.armeria.common.annotation.UnstableApi;
+import com.linecorp.armeria.internal.common.TimeoutExceptionPredicate;
 
 /**
  * A skeletal builder implementation for {@link RetryRule}, {@link RetryRuleWithContent},
@@ -257,8 +258,7 @@ public SELF onTimeoutException() {
             if (ctx.isTimedOut()) {
                 return true;
             }
-            return ex instanceof TimeoutException ||
-                   ex instanceof UnprocessedRequestException && ex.getCause() instanceof TimeoutException;
+            return TimeoutExceptionPredicate.isTimeoutException(ex);
         });
     }
 

core/src/main/java/com/linecorp/armeria/client/ClientRequestContext.java

@@ -49,6 +49,7 @@
 import com.linecorp.armeria.common.util.SafeCloseable;
 import com.linecorp.armeria.common.util.TimeoutMode;
 import com.linecorp.armeria.internal.common.RequestContextUtil;
+import com.linecorp.armeria.internal.common.TimeoutExceptionPredicate;
 import com.linecorp.armeria.server.ServiceRequestContext;
 
 import io.netty.util.Attribute;
@@ -525,8 +526,7 @@ default boolean isTimedOut() {
             return true;
         }
         final Throwable cause = cancellationCause();
-        return cause instanceof TimeoutException ||
-               cause instanceof UnprocessedRequestException && cause.getCause() instanceof TimeoutException;
+        return TimeoutExceptionPredicate.isTimeoutException(cause);
     }
 
     /**

core/src/main/java/com/linecorp/armeria/internal/common/TimeoutExceptionPredicate.java

@@ -0,0 +1,67 @@
+/*
+ * Copyright 2025 LINE Corporation
+ *
+ * LINE Corporation licenses this file to you 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 com.linecorp.armeria.internal.common;
+
+import com.linecorp.armeria.client.UnprocessedRequestException;
+import com.linecorp.armeria.common.TimeoutException;
+import com.linecorp.armeria.common.annotation.Nullable;
+import com.linecorp.armeria.common.util.Exceptions;
+import com.linecorp.armeria.internal.client.dns.DnsUtil;
+
+import io.netty.channel.ConnectTimeoutException;
+import io.netty.handler.proxy.ProxyConnectException;
+
+public final class TimeoutExceptionPredicate {
+
+    public static boolean isTimeoutException(@Nullable Throwable cause) {
+        if (cause == null) {
+            return false;
+        }
+        cause = peel(cause);
+
+        if (cause instanceof TimeoutException) {
+            // Armeria timeout.
+            return true;
+        }
+        if (cause instanceof ConnectTimeoutException) {
+            // A connection level timeout.
+            return true;
+        }
+
+        if (cause instanceof ProxyConnectException) {
+            // https://github.com/netty/netty/blob/0138f2335593d50e3eb1d8e0e97d3e8438f7a74d/handler-proxy/src/main/java/io/netty/handler/proxy/ProxyHandler.java#L201
+            final String message = cause.getMessage();
+            // TODO(ikhoon): Consider sending a PR to Netty to add a dedicated exception type for this.
+            if (message != null && message.contains("timeout")) {
+                return true;
+            }
+        }
+        // A DNS level timeout.
+        return DnsUtil.isDnsQueryTimedOut(cause);
+    }
+
+    private static Throwable peel(Throwable cause) {
+        cause = Exceptions.peel(cause);
+        if (cause instanceof UnprocessedRequestException) {
+            cause = cause.getCause();
+        }
+        assert cause != null;
+        return cause;
+    }
+
+    private TimeoutExceptionPredicate() {}
+}

core/src/test/java/com/linecorp/armeria/internal/common/TimeoutExceptionPredicateTest.java

@@ -0,0 +1,54 @@
+/*
+ * Copyright 2025 LINE Corporation
+ *
+ * LINE Corporation licenses this file to you 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 com.linecorp.armeria.internal.common;
+
+import static com.linecorp.armeria.internal.common.TimeoutExceptionPredicate.isTimeoutException;
+import static org.assertj.core.api.Assertions.assertThat;
+
+import org.junit.jupiter.api.Test;
+
+import com.linecorp.armeria.client.DnsTimeoutException;
+import com.linecorp.armeria.client.UnprocessedRequestException;
+import com.linecorp.armeria.internal.testing.AnticipatedException;
+import com.linecorp.armeria.server.RequestTimeoutException;
+
+import io.netty.channel.ConnectTimeoutException;
+import io.netty.handler.proxy.ProxyConnectException;
+
+class TimeoutExceptionPredicateTest {
+
+    @Test
+    void testTimeoutException() {
+        assertThat(isTimeoutException(new ConnectTimeoutException())).isTrue();
+        assertThat(isTimeoutException(RequestTimeoutException.get())).isTrue();
+        assertThat(isTimeoutException(new DnsTimeoutException("test"))).isTrue();
+        assertThat(isTimeoutException(new ProxyConnectException("timeout"))).isTrue();
+    }
+
+    @Test
+    void unwrapUnprocessedException() {
+        UnprocessedRequestException unprocessedException =
+                UnprocessedRequestException.of(new ConnectTimeoutException());
+        assertThat(isTimeoutException(unprocessedException)).isTrue();
+
+        unprocessedException = UnprocessedRequestException.of(new ProxyConnectException("... timeout"));
+        assertThat(isTimeoutException(unprocessedException)).isTrue();
+
+        unprocessedException = UnprocessedRequestException.of(new AnticipatedException());
+        assertThat(isTimeoutException(unprocessedException)).isFalse();
+    }
+}