In BBEdit how do you set the syntax coloring for a document that is unsaved and has no extension?
The language setting is in the status bar at the bottom of the editing view. For new untitled documents it says "(none)", click there to open a menu from which you can choose your desired language.
If you always want a specific language for untitled documents, there is an expert preference, which you can set with this Terminal command (for example, setting it to Markdown):
defaults write com.barebones.bbedit DefaultLanguageNameForNewDocuments -string "Markdown"
In quotes instead of "Markdown" you can use the human-readable name of the language as it appears in the menu.