"Get" + "married" can be either an adjectival passive or a verbal one:
In the former, "married" is an adjective; in the latter a past participle verb.
[1] They are hoping to get married by the bishop. (verbal passive)
[2] They are getting married at the weekend. (adjectival)
In [1] the by phrase makes it clearly verbal, so "married" is a verb here. In [2] there is no explicit or implicit agent, and even though "married" (unlike "engaged"), cannot combine with "become" (*“They became married”), "married" is still an adjective here with a meaning similar to "They are marrying each other".
[3] They got engaged last month.
"Get" + "engaged" is always an adjectival passive. "Engaged" is morphologically related to the past participle verb, but its meaning has changed so it is no longer comparable to a verbal passive. Further evidence of adjectivehood comes from the fact that it can combine with “become”, as in “They became engaged last month”. Only adjectives can combine with “become”.