What part-of-speech is "all" in these sentences?

These different dictionarys don't agree about what part-of-speech "all" is when it goes between subject and verb:

For Cambridge dictionary is an adverb

• The kids all go to school on the same bus. link

For Macmillan dictionary is a pronoun

• These buildings all belong to the college. link

For Merrian-Webster dictionary is an adjective

• They all came late.
• We all need to work faster. link

I am a little confused about them. Can some of you explain them? Thanks for your answers

This has come up before here. "All" in these examples is a floated quantifier, produced by the transformation "Quantifier Float". However, if you think that this rule functions to convert a quantifier into an adverb, then it is also reasonable to classify it as an adverb. McCawley discusses this in Syntactic Phen. and argues that the special case of "all" after a pronoun is from a different rule: Quantifier Pronoun Flip.