Is None of those bagels look fresh a relative pronoun?

No, the pronoun in the sentence "None of those bagels look fresh." is 'none' an indefinite pronoun.

The pronoun 'none' is a Word for 'not any', 'not one'.

Note: the Word 'those' is a demonstrative pronoun when it takes the place of a noun, but in the example sentence, the Word 'those' is functioning as an adjective, placed before the noun to describe the noun 'bagels'.