perf(git): cache git rev-parse results within sessions

Multiple gt commands call git rev-parse --show-toplevel, adding ~50ms
each invocation. Results rarely change within a session, and multiple
agents calling git concurrently contend on .git/index.lock.

Add cached RepoRoot() and RepoRootFrom() functions to the git package
and update all callers to use them. This ensures a single git subprocess
call per process for the common case of checking the current directory's
repo root.

Files updated:
- internal/git/git.go: Add RepoRoot() and RepoRootFrom()
- internal/cmd/prime.go: Use cached git.RepoRoot()
- internal/cmd/molecule_status.go: Use cached git.RepoRoot()
- internal/cmd/sling_helpers.go: Use cached git.RepoRoot()
- internal/cmd/rig_quick_add.go: Use git.RepoRootFrom() for path arg
- internal/version/stale.go: Use cached git.RepoRoot()

Closes: bd-2zd.5

internal/cmd/molecule_status.go

@@ -4,13 +4,13 @@ import (
 	"encoding/json"
 	"fmt"
 	"os"
-	"os/exec"
 	"path/filepath"
 	"strings"
 
 	"github.com/spf13/cobra"
 	"github.com/steveyegge/gastown/internal/beads"
 	"github.com/steveyegge/gastown/internal/config"
+	"github.com/steveyegge/gastown/internal/git"
 	"github.com/steveyegge/gastown/internal/style"
 	"github.com/steveyegge/gastown/internal/workspace"
 )
@@ -963,13 +963,9 @@ func outputMoleculeCurrent(info MoleculeCurrentInfo) error {
 }
 
 // getGitRootForMolStatus returns the git root for hook file lookup.
+// Uses cached value to avoid repeated git subprocess calls.
 func getGitRootForMolStatus() (string, error) {
-	cmd := exec.Command("git", "rev-parse", "--show-toplevel")
-	out, err := cmd.Output()
-	if err != nil {
-		return "", err
-	}
-	return strings.TrimSpace(string(out)), nil
+	return git.RepoRoot()
 }
 
 // isTownLevelRole returns true if the agent ID is a town-level role.

internal/cmd/prime.go

@@ -11,6 +11,7 @@ import (
 
 	"github.com/spf13/cobra"
 	"github.com/steveyegge/gastown/internal/beads"
+	"github.com/steveyegge/gastown/internal/git"
 	"github.com/steveyegge/gastown/internal/lock"
 	"github.com/steveyegge/gastown/internal/state"
 	"github.com/steveyegge/gastown/internal/style"
@@ -544,13 +545,9 @@ func buildRoleAnnouncement(ctx RoleContext) string {
 }
 
 // getGitRoot returns the root of the current git repository.
+// Uses cached value to avoid repeated git subprocess calls.
 func getGitRoot() (string, error) {
-	cmd := exec.Command("git", "rev-parse", "--show-toplevel")
-	out, err := cmd.Output()
-	if err != nil {
-		return "", err
-	}
-	return strings.TrimSpace(string(out)), nil
+	return git.RepoRoot()
 }
 
 // getAgentIdentity returns the agent identity string for hook lookup.

internal/cmd/rig_quick_add.go

@@ -11,6 +11,7 @@ import (
 	"strings"
 
 	"github.com/spf13/cobra"
+	"github.com/steveyegge/gastown/internal/git"
 	"github.com/steveyegge/gastown/internal/style"
 	"github.com/steveyegge/gastown/internal/workspace"
 )
@@ -138,13 +139,7 @@ func runRigQuickAdd(cmd *cobra.Command, args []string) error {
 }
 
 func findGitRoot(path string) (string, error) {
-	cmd := exec.Command("git", "rev-parse", "--show-toplevel")
-	cmd.Dir = path
-	out, err := cmd.Output()
-	if err != nil {
-		return "", err
-	}
-	return strings.TrimSpace(string(out)), nil
+	return git.RepoRootFrom(path)
 }
 
 func findGitRemoteURL(gitRoot string) (string, error) {

internal/cmd/sling_helpers.go

@@ -10,6 +10,7 @@ import (
 
 	"github.com/steveyegge/gastown/internal/beads"
 	"github.com/steveyegge/gastown/internal/constants"
+	"github.com/steveyegge/gastown/internal/git"
 	"github.com/steveyegge/gastown/internal/tmux"
 	"github.com/steveyegge/gastown/internal/workspace"
 )
@@ -378,13 +379,13 @@ func ensureAgentReady(sessionName string) error {
 }
 
 // detectCloneRoot finds the root of the current git clone.
+// Uses cached value to avoid repeated git subprocess calls.
 func detectCloneRoot() (string, error) {
-	cmd := exec.Command("git", "rev-parse", "--show-toplevel")
-	out, err := cmd.Output()
+	root, err := git.RepoRoot()
 	if err != nil {
 		return "", fmt.Errorf("not in a git repository")
 	}
-	return strings.TrimSpace(string(out)), nil
+	return root, nil
 }
 
 // detectActor returns the current agent's actor string for event logging.