feat(tui-go): health-checks pane

Surface the health subsystem (llama/event-store/disk probes) in the TUI,
mirroring the session-stats pane: ClientMessage.GetHealthChecks ->
ServerMessage.HealthChecks (health.checks, reuses HealthReport) ->
StreamQueries.healthChecks via HealthInspectionService; Go OverlayHealth on
key H + palette 'health checks', pull-based fetch, per-subject status with
degraded loud. Empty/disabled -> visible fallback (no blank/lie). Go+Kotlin
golden tests pin the wire contract field-for-field. Observability spec §4/§3.

apps/tui-go/internal/protocol/protocol.go

@@ -55,6 +55,7 @@ const (
 	TypeConfigSnapshot   = "config.snapshot"
 	TypeSessionStats     = "session.stats"
 	TypeIdeaList         = "idea.list"
+	TypeHealthChecks     = "health.checks"
 )
 
 // ServerMessage is a flat decode of every server->client variant. Field names
@@ -139,6 +140,9 @@ type ServerMessage struct {
 	// session.stats — derived metrics for a session (reply to GetSessionStats)
 	Stats *StatsDto `json:"stats"`
 
+	// health.checks — system health report (reply to GetHealthChecks)
+	Health *HealthDto `json:"health"`
+
 	// clarification.required — open questions a stage raised for the operator
 	Questions []ClarificationQuestionDto `json:"questions"`
 
@@ -242,6 +246,26 @@ type FailureMetricsDto struct {
 	WorkflowFailures  int64 `json:"workflowFailures"`
 }
 
+// HealthSubjectDto is one monitored subject's health status. Mirrors Kotlin HealthSubjectReport.
+// status is "HEALTHY" or "DEGRADED"; since is an ISO-8601 string for the last edge event.
+type HealthSubjectDto struct {
+	Subject       string `json:"subject"`
+	Status        string `json:"status"`
+	Metric        string `json:"metric"`
+	ObservedValue int64  `json:"observedValue"`
+	Detail        string `json:"detail"`
+	Since         string `json:"since"`
+}
+
+// HealthDto is the system health snapshot. Mirrors Kotlin HealthReport.
+// overall is "HEALTHY" or "DEGRADED". subjects is empty when health monitoring is disabled
+// or no probes have fired yet — the TUI renders a visible fallback in that case.
+type HealthDto struct {
+	Overall   string             `json:"overall"`
+	Subjects  []HealthSubjectDto `json:"subjects"`
+	CheckedAt string             `json:"checkedAt"`
+}
+
 type ConfigFieldDto struct {
 	Key             string   `json:"key"`
 	Type            string   `json:"type"`
@@ -465,3 +489,8 @@ func CreateGrant(sessionID, scope string, permittedTiers []string, reason, toolN
 func Hello(workingDir string) []byte {
 	return encode("Hello", map[string]any{"workingDir": workingDir})
 }
+
+// GetHealthChecks requests the system health-check report (replied to with health.checks).
+func GetHealthChecks() []byte {
+	return encode("GetHealthChecks", map[string]any{})
+}