No, it really should be "Introducing Dark Mode (beta) for Stack Overflow"
Also, Stack Overflow is two words.
Both are grammatically correct. "has now" gives emphasis to "now" while "now has" emphasizes "has".
While adverbs can come after an action verb (in this case, 'has' functions as an act of a possession), as a native English speaker and a former ESL instructor I have NEVER heard the phrase "has now" or any similar phrases such as, "he has finally a car". They both sound extremely awkward.