Implement liveness BeaconAPI (#4343)

## Issue Addressed

#4243

## Proposed Changes

- create a new endpoint for liveness/{endpoint}

## Additional Info
This is my first PR.

beacon_node/http_api/tests/tests.rs

@@ -2980,6 +2980,69 @@ impl ApiTester {
         self
     }
 
+    pub async fn test_post_validator_liveness_epoch(self) -> Self {
+        let epoch = self.chain.epoch().unwrap();
+        let head_state = self.chain.head_beacon_state_cloned();
+        let indices = (0..head_state.validators().len())
+            .map(|i| i as u64)
+            .collect::<Vec<_>>();
+
+        // Construct the expected response
+        let expected: Vec<StandardLivenessResponseData> = head_state
+            .validators()
+            .iter()
+            .enumerate()
+            .map(|(index, _)| StandardLivenessResponseData {
+                index: index as u64,
+                is_live: false,
+            })
+            .collect();
+
+        let result = self
+            .client
+            .post_validator_liveness_epoch(epoch, indices.clone())
+            .await
+            .unwrap()
+            .data;
+
+        assert_eq!(result, expected);
+
+        // Attest to the current slot
+        self.client
+            .post_beacon_pool_attestations(self.attestations.as_slice())
+            .await
+            .unwrap();
+
+        let result = self
+            .client
+            .post_validator_liveness_epoch(epoch, indices.clone())
+            .await
+            .unwrap()
+            .data;
+
+        let committees = head_state
+            .get_beacon_committees_at_slot(self.chain.slot().unwrap())
+            .unwrap();
+        let attesting_validators: Vec<usize> = committees
+            .into_iter()
+            .flat_map(|committee| committee.committee.iter().cloned())
+            .collect();
+        // All attesters should now be considered live
+        let expected = expected
+            .into_iter()
+            .map(|mut a| {
+                if attesting_validators.contains(&(a.index as usize)) {
+                    a.is_live = true;
+                }
+                a
+            })
+            .collect::<Vec<_>>();
+
+        assert_eq!(result, expected);
+
+        self
+    }
+
     // Helper function for tests that require a valid RANDAO signature.
     async fn get_test_randao(&self, slot: Slot, epoch: Epoch) -> (u64, SignatureBytes) {
         let fork = self.chain.canonical_head.cached_head().head_fork();
@@ -4870,6 +4933,14 @@ async fn builder_works_post_capella() {
         .await;
 }
 
+#[tokio::test(flavor = "multi_thread", worker_threads = 2)]
+async fn post_validator_liveness_epoch() {
+    ApiTester::new()
+        .await
+        .test_post_validator_liveness_epoch()
+        .await;
+}
+
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
 async fn lighthouse_endpoints() {
     ApiTester::new()