Are "The Purloined Letter" and "Bartleby the Scrivener" written with a third person omniscient narrator?

Edgar Allen Poe's "The Purloined Letter" uses a first
person narrator who, by definition, participates in the story and only knows his own
motives, thoughts, perceptions, feelings, and
emotions:

At
Paris, just after dark one gusty evening in the autumn of 18--, I was enjoying the
twofold luxury of meditation and a meerschaum,
...

Herman Mellville's short
story "Bartleby the Scrivener: A Tale of Wall Street" also uses a first person narrator
who is, also by definition, a participant in the story and only knowledgeable about his
own thoughts, motives, feelings, perceptions, and
emotions:

I AM
a rather elderly man. The nature of my avocations for the last thirty years has brought
me into more than ordinary contact with . . . the law-copyists . .
.

In first person narration,
the narrator refers to her-/-imself as "I," and the narrator only knows about the inner
world of other characters if they tell her/him, if s/he infers or deduces or guesses at
it, or if they read a letter or a diary entry or explanatory article etc, or if some
other character tells them something about it.

Third person
omniscient narration differs greatly from first person because the narrative is told by
someone who is not a participant in the story and has the ability to know the inner
world of any character, thus can tell the thoughts, feelings, perceptions, motives,
emotions of any character, and can tell the story through the experience of any
character at any moment in the narrative (change the point of view at any time). As can
be seen, by this definition neither Poe's story nor Melville's story has a third person
omniscient narrator.