The characters in the Watchmen comic are original creations. So it wasn’t pre-existing DC characters like Batman etc. It was then adapted into a film and now a TV show has been made that’s a sequel to the events of the comic.
Watchmen was pitched using the Question, Blue Beetle, PeaceMaker, Captain Atom etc. DC changed their minds, and these analogues were born.
If anyone s interested in the original characters in the style of Watchmen, check out Pax Americana, written by Grant Morrison and art by Frank Quitely. It was part of the miniseries Multiversity.