Its not Edge New tab anymore, but a different webpage. If you choose "Always Show", it will show up on that page too. Otherwise, how does Edge know your extension page is a substitute New Tab? Tabs content vary... :smiling_face_with_smiling_eyes:
What can fix it is adding an option in New Tab Settings "Set a webpage as New Tab". It can be an option in a dedicated Tab Control section in Settings that includes tab grouping, tree, switching, close and open order, new tab options.