Local Tasks menu is shown even when the tray is empty

Able to re[roduced the issue but wheen tried to apply the patch, it's showing:
Skipped patch 'admin_toolbar_tools/admin_toolbar_tools.module'.

Patch rerolled.

Verified the patch #5 and tested it on Drupal version 10.1.x and Admin Toolbar version 3.x. The patch works fine and I have added the before and after screenshots for reference.

With the use of a render placeholder, it seems we're losing the performance benefit by also checking for the local tasks here. I would recommend testing the patch in 🐛 Local tasks display tabs disappear Fixed instead which also solves this and some of the missing caching metadata around the local tasks.