fix: address PR review findings (Bug 1-3 + sidebar minor)

Bug 1 (runtime_events.go): use msg.ConfigPath instead of
constructing 'budget.' + msg.Limit; named budget paths like
'budgets.tight.max_cost' now display correctly.

Bug 2 (types.go): MaxTime comment updated from 'wall-clock
duration' to 'working time — cumulative turn durations; idle
time does not count'.

Bug 3 (docs/configuration/budget/index.md): three occurrences
of 'wall-clock time' changed to 'working time' (front-matter
description, lede paragraph, and example heading).

Minor (sidebar.go): removed duplicate first comment block from
formatBudgetDuration.

Author: aheritier

docs/configuration/budget/index.md

@@ -1,12 +1,12 @@
 ---
 title: "Budget"
-description: "Cap what a single run may spend in money, tokens, or wall-clock time."
+description: "Cap what a single run may spend in money, tokens, or working time."
 keywords: docker agent, ai agents, configuration, yaml, budget, cost, limits
 weight: 75
 canonical: https://docs.docker.com/ai/docker-agent/configuration/budget/
 ---
 
-_Cap what a single run may spend in money, tokens, or wall-clock time._
+_Cap what a single run may spend in money, tokens, or working time._
 
 ## Overview
 
@@ -176,7 +176,7 @@ budget:
   max_cost: 5.00
 ```
 
-Cap wall-clock time for an unattended job:
+Cap working time for an unattended job:
 
 ```yaml
 agents:

pkg/config/latest/types.go

@@ -88,7 +88,9 @@ type BudgetConfig struct {
 	// compaction resets — those measure current context length, not spend.
 	MaxTokens int64 `json:"max_tokens,omitempty" yaml:"max_tokens,omitempty"`
 
-	// MaxTime is the maximum wall-clock duration of the run, in Go
+	// MaxTime is the maximum working time for the run — the cumulative
+	// sum of turn durations, not wall-clock since the session opened.
+	// Idle time while the user reads and types does not count. In Go
 	// duration format ("10m", "30s", "1h30m").
 	//
 	// It is checked at turn boundaries, so a run stops at the first

pkg/tui/components/sidebar/sidebar.go

@@ -1866,8 +1866,6 @@ func budgetPartStyle(used, limit float64) lipgloss.Style {
 	return contextGaugeStyle(level, styles.TabAccentStyle)
 }
 
-// formatBudgetDuration renders whole seconds, so a live reading doesn't
-// jitter with sub-second noise.
 // formatBudgetDuration renders a whole-second reading compactly, dropping
 // zero components so a round ceiling reads "10m" and "1h" rather than
 // Duration.String's "10m0s" and "1h0m0s" — the budget column is the

pkg/tui/page/chat/runtime_events.go

@@ -452,7 +452,7 @@ func (p *chatPage) handleToolCallResponse(msg *runtime.ToolCallResponseEvent) te
 func (p *chatPage) handleBudgetExceeded(msg *runtime.BudgetExceededEvent) tea.Cmd {
 	spinnerCmd := p.setWorking(false)
 	warnCmd := notification.WarningCmd(fmt.Sprintf(
-		"Run stopped by budget.%s — used %s of %s.", msg.Limit, msg.Used, msg.Max,
+		"Run stopped by %s — used %s of %s.", msg.ConfigPath, msg.Used, msg.Max,
 	))
 	return tea.Batch(spinnerCmd, warnCmd)
 }