Q: Text Edit document  word count?

Not natively, however easy enough to use AppleScript

see: TextEdit word count

An alternative is  another light wait text editor Bean which has native word count

(it appears latest development  was 2013, but you could try it?)

TextEdit word count

Nice CT !

Here is the following through for clarrification:

Start with a blank search field after you pull up with command F.

If no "insert pattern" then select "full word".  This seems to work for both plain.txt and rich text.rtf