Feature Request: add more visibility/stats in Tablet Throttler

[shlomi-noach]

Feature Description

The table throttler exposes some useful stats/metrics today, such as:

• Number of checks made
• Check errors
• Probes latency
• etc.

Combined with "HeartbeatWrites" stats we can get a picture of throttler state.

However, for more fine grained analysis, and especially where --heartbeat_on_demand_duration is used, we also want to know:

• When a tablet throttler was "recently checked"
• When a PRIMARY tablet throttler identifies that shard/replica tables have been "recently checked" (via CheckThrottlerResponse)
• When the throttler actively requests heartbeat lease.

See #13195 which introduced the RecentlyChecked indicator.

Use Case(s)

Analyzing table throttler behavior.