Whose idea was it to make the full-screen button hide the taskbar forever?

Full-screen mode and a maximized window are different. Full-screen deliberately uses the display area for the application; maximizing a normal window is usually the better choice when you want the taskbar available while multitasking.

First leave full-screen using the application’s own control. In Microsoft Edge, F11 toggles full-screen off and on; other applications can use different shortcuts or a windowed mode setting. Then maximize the window, for example with Windows+Up, and check Settings > Personalization > Taskbar > Taskbar behaviors. Clear Automatically hide the taskbar if you want it visible during ordinary desktop use.

While an app is full-screen, Alt+Tab can switch applications and Windows+N opens notification center. The auto-hide setting is not a universal override for an application’s full-screen presentation. If the taskbar stays missing after leaving full-screen, that is a separate issue: identify the application and whether it happens with other apps before changing Windows settings further.