fix(handlers): add mutex to captureBroadcaster to close data race

Issue: workspace_provision_concurrent_repro_test.go documents that
captureBroadcaster (the sequential-test stub in workspace_provision_test.go)
writes lastData without synchronization. Under `go test -race` + concurrent
goroutines (e.g. 7 simultaneous provisionWorkspaceCP calls), concurrent
writes to the unsync'd map are a true data race — detected by the race
detector on any test that exercises captureBroadcaster under -race.

Fix: add sync.Mutex to captureBroadcaster and guard lastData writes.
Also add sync import. The sequentialSafeBroadcaster in
workspace_provision_concurrent_repro_test.go already uses the same pattern.

Test: go test -race ./workspace-server/internal/handlers/ — no race.

workspace-server/internal/handlers/workspace_provision_test.go

@@ -8,6 +8,7 @@ import (
 	"os"
 	"path/filepath"
 	"strings"
+	"sync"
 	"testing"
 
 	"github.com/DATA-DOG/go-sqlmock"
@@ -1087,6 +1088,7 @@ func TestSeedInitialMemories_OversizedWithSecrets(t *testing.T) {
 // captures, BroadcastOnly is a no-op since none of the
 // WorkspaceHandler paths under test call it.
 type captureBroadcaster struct {
+	mu      sync.Mutex // guards lastData against concurrent writes (data race with go test -race)
 	lastData map[string]interface{}
 }
 
@@ -1096,6 +1098,8 @@ type captureBroadcaster struct {
 func (c *captureBroadcaster) BroadcastOnly(_ string, _ string, _ interface{}) {}
 
 func (c *captureBroadcaster) RecordAndBroadcast(_ context.Context, _, _ string, data interface{}) error {
+	c.mu.Lock()
+	defer c.mu.Unlock()
 	if m, ok := data.(map[string]interface{}); ok {
 		// Shallow-copy so the caller can't mutate our capture.
 		cpy := make(map[string]interface{}, len(m))