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Something stuck. We can unstick it.
Write with your macOS or Windows version, which Mac or PC you have, and whether the overlay appears when you hold the shortcut.
The usual permissions
On a Mac: System Settings → Privacy & Security → Microphone, and Accessibility. Without Accessibility, VV can hear you and still cannot paste.
On Windows: Settings → Privacy & security → Microphone, with desktop apps allowed. That is the only permission Vaitly Voice needs there. Windows does not let an ordinary program type into a window running as administrator, such as an elevated command prompt or Task Manager, so dictation does nothing in those.
If a second copy of VV is running, the first instance wins. Quit from the menu bar (on Windows, the icon in the notification area), then open the one you meant.