If you're definitely referring to your laptop's taskbar (at the foot of the screen), rather than to a toolbar (within the Edge window), I can't think of any reason why an update to Edge should have affected it.
However the icons on your taskbar are simply shortcuts to different programs. If you know which program you use to access your emails (such as Mail, Thunderbird or whatever), it's dead easy to put a shortcut onto the taskbar again. Simply click on the Start button, at the bottom left of your screen and go the list of programs on your computer. Scroll down to the relevant program and RIGHT-click on it. Then select More > Pin to Taskbar. Job done.