[bridge] log last synced eth blocks and default to end block (#19507)

## Description 

as title


## Test plan 

How did you test the new or updated feature?

---

## Release notes

Check each box that your changes affect. If none of the boxes relate to
your changes, release notes aren't required.

For each box you select, include information after the relevant heading
that describes the impact of your changes that a user might notice and
any actions they must take to implement updates.

- [ ] Protocol: 
- [ ] Nodes (Validators and Full nodes): 
- [ ] Indexer: 
- [ ] JSON-RPC: 
- [ ] GraphQL: 
- [ ] CLI: 
- [ ] Rust SDK:
- [ ] REST API:

bridge/runbook/validator_runbook.md

@@ -131,7 +131,7 @@ To enable `bridge_client` feature on a `BridgeNode`, set the following parameter
 run-client: true
 db-path: <PATH_TO_DB>
 sui:
-    bridge-client-key-path: <PATH_TO_BRIDGE_CLIENT_KEY>  # optional, when absent, use bridge-authority-key-path as the keypair for BridgeClient
+    bridge-client-key-path: <PATH_TO_BRIDGE_CLIENT_KEY>
 ```
 
 
@@ -184,3 +184,35 @@ Test ingress with curl on a remote machine and expect a `200` response:
 ```bash
 $ curl -v {YOUR_BRIDGE_URL}
 ```
+
+### Bridge Node Monitoring
+(This section is still WIP)
+
+* Use `uptime` to check if the node is running.
+
+* A full list of Bridge Node metrics can be found [here](../../crates/sui-bridge/src/metrics.rs). Find descriptions of each metric [here](../../crates/sui-bridge/src/metrics.rs) and we skip them below.
+
+#### When `run-client: false`
+In this case Bridge Node runs as a passive observer and does not proactively poll onchain activities. Important metrics to monitor in this case are the request handling metrics such as
+* `bridge_requests_received`
+* `bridge_requests_ok`
+* `bridge_err_requests`
+* `bridge_requests_inflight`
+* `bridge_eth_rpc_queries`
+* `bridge_eth_rpc_queries_latency`
+* `bridge_signer_with_cache_hit`
+* `bridge_signer_with_cache_miss`
+* `bridge_sui_rpc_errors`
+
+#### When `run-client: true`
+In this case Bridge Client is toggled on and syncs with Blockchains proactively. The best ones to track progress are:
+* `bridge_last_synced_sui_checkpoints`
+* `bridge_last_synced_eth_blocks`
+* `bridge_last_finalized_eth_block`
+* `bridge_sui_watcher_received_events`
+* `bridge_eth_watcher_received_events`
+* `bridge_sui_watcher_received_actions`
+* `bridge_eth_watcher_received_actions`
+
+It's also critical to track the balance of your client gas coin, and top up once it dips below a certain threshold:
+* `bridge_gas_coin_balance`

crates/sui-bridge/src/eth_syncer.rs

@@ -196,12 +196,10 @@ where
                     "Observed {len} new Eth events",
                 );
             }
-            if let Some(last_block) = last_block {
-                metrics
-                    .last_synced_eth_blocks
-                    .with_label_values(&[&contract_address_str])
-                    .set(last_block as i64);
-            }
+            metrics
+                .last_synced_eth_blocks
+                .with_label_values(&[&contract_address_str])
+                .set(last_block.unwrap_or(end_block) as i64);
             start_block = end_block + 1;
         }
     }