feat(synthesis): Add synthesis step for convoy formulas (gt-v5s0j)

Implements the synthesis step that combines leg outputs into a final
deliverable for convoy workflows:

- `gt synthesis start <convoy-id>` - Start synthesis after verifying
  all legs are complete, collecting outputs, and slinging to polecat
- `gt synthesis status <convoy-id>` - Show synthesis readiness and
  leg completion status
- `gt synthesis close <convoy-id>` - Close convoy after synthesis

Key features:
- Collects leg outputs from formula-defined paths (e.g., findings.md)
- Creates synthesis bead with combined context from all leg outputs
- Integrates with formula.toml synthesis configuration
- Provides TriggerSynthesisIfReady() for automated synthesis trigger
- Adds SynthesisFields struct for tracking synthesis state in beads

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/beads/fields.go

@@ -344,6 +344,87 @@ func SetMRFields(issue *Issue, fields *MRFields) string {
 	return formatted + "\n\n" + strings.Join(otherLines, "\n")
 }
 
+// SynthesisFields holds structured fields for synthesis beads.
+// These fields track the synthesis step in a convoy workflow.
+type SynthesisFields struct {
+	ConvoyID   string `json:"convoy_id"`   // Parent convoy ID
+	ReviewID   string `json:"review_id"`   // Review ID for output paths
+	OutputPath string `json:"output_path"` // Path to synthesis output file
+	Formula    string `json:"formula"`     // Formula name (if from formula)
+}
+
+// ParseSynthesisFields extracts synthesis fields from an issue's description.
+// Fields are expected as "key: value" lines. Returns nil if no fields found.
+func ParseSynthesisFields(issue *Issue) *SynthesisFields {
+	if issue == nil || issue.Description == "" {
+		return nil
+	}
+
+	fields := &SynthesisFields{}
+	hasFields := false
+
+	for _, line := range strings.Split(issue.Description, "\n") {
+		line = strings.TrimSpace(line)
+		if line == "" {
+			continue
+		}
+
+		colonIdx := strings.Index(line, ":")
+		if colonIdx == -1 {
+			continue
+		}
+
+		key := strings.TrimSpace(line[:colonIdx])
+		value := strings.TrimSpace(line[colonIdx+1:])
+		if value == "" {
+			continue
+		}
+
+		switch strings.ToLower(key) {
+		case "convoy", "convoy_id", "convoy-id":
+			fields.ConvoyID = value
+			hasFields = true
+		case "review_id", "review-id", "reviewid":
+			fields.ReviewID = value
+			hasFields = true
+		case "output_path", "output-path", "outputpath":
+			fields.OutputPath = value
+			hasFields = true
+		case "formula":
+			fields.Formula = value
+			hasFields = true
+		}
+	}
+
+	if !hasFields {
+		return nil
+	}
+	return fields
+}
+
+// FormatSynthesisFields formats SynthesisFields as a string for issue description.
+func FormatSynthesisFields(fields *SynthesisFields) string {
+	if fields == nil {
+		return ""
+	}
+
+	var lines []string
+	if fields.ConvoyID != "" {
+		lines = append(lines, "convoy: "+fields.ConvoyID)
+	}
+	if fields.ReviewID != "" {
+		lines = append(lines, "review_id: "+fields.ReviewID)
+	}
+	if fields.OutputPath != "" {
+		lines = append(lines, "output_path: "+fields.OutputPath)
+	}
+	if fields.Formula != "" {
+		lines = append(lines, "formula: "+fields.Formula)
+	}
+
+	return strings.Join(lines, "\n")
+}
+
 // RoleConfig holds structured lifecycle configuration for role beads.
 // These fields are stored as "key: value" lines in the role bead description.
 // This enables agents to self-register their lifecycle configuration,