by the way vs apropos

by the way is not an adjective while apropos is an adjective.

Word	Noun	Adjective	Verb	Adverb
by the way	No	No	No	Yes
apropos	No	Yes	No	Yes

As adverbs, by the way and apropos are synonyms defined as:

Other synonyms of by the way include by the bye, incidentally.

by the way (adjective)	apropos (adjective)
	of an appropriate or pertinent nature

by the way (adverb)	apropos (adverb)
introducing a different topic	at an opportune time
	introducing a different topic