fix: address Playwright API audit findings

- Replace deprecated Locator.Type() with PressSequentially() (node.go)
- Close page on Goto failure to prevent resource leak (playwright.go)
- Fix teardown order: close context before browser (playwright.go)
- Clean up resources on NewPage failure (interactive.go)
- Spawn cleanup goroutine on context cancellation in both constructors

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

playwright.go

@@ -195,6 +195,12 @@ func NewBrowser(ctx context.Context, opts ...BrowserOptions) (Browser, error) {
 
 	select {
 	case <-ctx.Done():
+		go func() {
+			r := <-resultCh
+			if r.err == nil && r.browser != nil {
+				_ = r.browser.Close()
+			}
+		}()
 		return nil, ctx.Err()
 	case result := <-resultCh:
 		return result.browser, result.err
@@ -242,6 +248,7 @@ func (b playWrightBrowser) openPage(_ context.Context, target string, opts OpenP
 
 	resp, err := page.Goto(target, pwOpts)
 	if err != nil {
+		_ = page.Close()
 		return nil, err
 	}
 
@@ -277,8 +284,8 @@ func (b playWrightBrowser) Open(ctx context.Context, url string, opts OpenPageOp
 
 func (b playWrightBrowser) Close() error {
 	return errors.Join(
-		b.browser.Close(),
 		b.ctx.Close(),
+		b.browser.Close(),
 		b.pw.Stop(),
 	)
 }