fix(install): Copy embedded formulas to new installations

When `gt install` creates a new HQ, formulas were not being provisioned
to `.beads/formulas/`. This embeds the formula library into the gt binary
and copies them during installation.

- Add go:generate directive to copy formulas from .beads/formulas/
- Add internal/formula/embed.go with ProvisionFormulas() function
- Call ProvisionFormulas() from runInstall() after beads init
- Add generate target to Makefile (build depends on it)
- Add TestInstallFormulasProvisioned integration test
- Log warning if formula stat fails with unexpected error

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

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

internal/formula/embed.go

@@ -0,0 +1,62 @@
+package formula
+
+import (
+	"embed"
+	"fmt"
+	"log"
+	"os"
+	"path/filepath"
+)
+
+// Generate formulas directory from canonical source at .beads/formulas/
+//go:generate sh -c "rm -rf formulas && mkdir -p formulas && cp ../../.beads/formulas/*.formula.toml ../../.beads/formulas/*.formula.json formulas/ 2>/dev/null || cp ../../.beads/formulas/*.formula.toml formulas/"
+
+//go:embed formulas/*.formula.toml formulas/*.formula.json
+var formulasFS embed.FS
+
+// ProvisionFormulas creates the .beads/formulas/ directory with embedded formulas.
+// This ensures new installations have the standard formula library.
+// If a formula already exists, it is skipped (no overwrite).
+// Returns the number of formulas provisioned.
+func ProvisionFormulas(beadsPath string) (int, error) {
+	entries, err := formulasFS.ReadDir("formulas")
+	if err != nil {
+		return 0, fmt.Errorf("reading formulas directory: %w", err)
+	}
+
+	// Create .beads/formulas/ directory
+	formulasDir := filepath.Join(beadsPath, ".beads", "formulas")
+	if err := os.MkdirAll(formulasDir, 0755); err != nil {
+		return 0, fmt.Errorf("creating formulas directory: %w", err)
+	}
+
+	count := 0
+	for _, entry := range entries {
+		if entry.IsDir() {
+			continue
+		}
+
+		destPath := filepath.Join(formulasDir, entry.Name())
+
+		// Skip if formula already exists (don't overwrite user customizations)
+		if _, err := os.Stat(destPath); err == nil {
+			continue
+		} else if !os.IsNotExist(err) {
+			// Log unexpected errors (e.g., permission denied) but continue
+			log.Printf("warning: could not check formula %s: %v", entry.Name(), err)
+			continue
+		}
+
+		content, err := formulasFS.ReadFile("formulas/" + entry.Name())
+		if err != nil {
+			return count, fmt.Errorf("reading %s: %w", entry.Name(), err)
+		}
+
+		if err := os.WriteFile(destPath, content, 0644); err != nil {
+			return count, fmt.Errorf("writing %s: %w", entry.Name(), err)
+		}
+		count++
+	}
+
+	return count, nil
+}