[lake/tiering] Add CoordinatorServer Monitoring Metrics for Lake Tiering Scheduling

[beryllw]

Purpose

Linked issue: close #2816

Brief change log

Scope: coordinator > lakeTiering (global)

Metric	Type	Description
pendingTablesCount	Gauge	Number of tables waiting to be tiered
runningTablesCount	Gauge	Number of tables currently being tiered

Tests

API and Format

Documentation

[Copilot]

Pull request overview

Adds global CoordinatorServer metrics to monitor lake tiering scheduling activity.

Changes:

• Introduces a LakeTieringMetricGroup and wires it into CoordinatorServer / LakeTableTieringManager.
• Registers two new gauges (pendingTablesCount, runningTablesCount) for lake tiering.
• Updates docs and tests to reflect/validate the new metrics.

Reviewed changes

Copilot reviewed 10 out of 10 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
website/docs/maintenance/observability/monitor-metrics.md	Documents the new lake tiering coordinator metrics.
fluss-server/src/main/java/org/apache/fluss/server/metrics/group/LakeTieringMetricGroup.java	Adds a dedicated metric group under the coordinator scope.
fluss-server/src/main/java/org/apache/fluss/server/coordinator/LakeTableTieringManager.java	Registers gauges + adjusts locking to support safe metric reads.
fluss-server/src/main/java/org/apache/fluss/server/coordinator/CoordinatorServer.java	Instantiates the tiering metric group and passes it to the manager.
fluss-common/src/main/java/org/apache/fluss/metrics/MetricNames.java	Adds metric name constants for the new gauges.
fluss-server/src/test/java/org/apache/fluss/server/metrics/group/TestingMetricGroups.java	Provides a reusable LakeTieringMetricGroup for tests.
fluss-server/src/test/java/org/apache/fluss/server/coordinator/LakeTableTieringManagerTest.java	Adds a test validating pending/running counts.
fluss-server/src/test/java/org/apache/fluss/server/coordinator/statemachine/TableBucketStateMachineTest.java	Updates construction of LakeTableTieringManager to pass the metric group.
fluss-server/src/test/java/org/apache/fluss/server/coordinator/rebalance/RebalanceManagerTest.java	Updates construction of LakeTableTieringManager to pass the metric group.
fluss-server/src/test/java/org/apache/fluss/server/coordinator/CoordinatorEventProcessorTest.java	Updates construction of LakeTableTieringManager to pass the metric group.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[luoyuxia]

@beryllw Thanks for the pr.
Please also close tieringMetricGroup in LakeTableTieringManager

[luoyuxia]

@beryllw Thanks for update. LGTM