The Edit menu : Speech menu item is for having selected/default text spoken to you. It has nothing to do with dictation.
There are two forms of Dictation capability in macOS Catalina. Regular dictation which is enabled in System Preferences : Keyboard panel : Dictation — where every word you speak must travel to Apple's servers to be interpreted as text and sent back to the current document, or text input field. One used to be able to enable enhanced dictation in the same location which performed all the dictation interpretation locally for speedier, but often less accurate results.
In Catalina, Apple has added Voice Control in System Preferences : Accessibility : Voice Control panel. This is a Siri Speech Recognition engine that takes the place of the old Enhanced Dictation, and also involves a hefty download of that software. The Siri speech engine only works for English speakers, and otherwise, the old Enhanced Dictation is used.
You can configure Voice Control using this Apple article, Use Voice Control on your Mac. It will take it awhile to adapt to your voice and speech patterns, and you can customize commands and vocabulary for it too, which are also shown in the preceding link.