And Mary said, "Behold, the Lord's handmaid. May it happen to me according to your word." And the angel departed from her.
I think that this is a very important & central issue, well summarized by the above quote of
Luke 1:38.
In the 7th century AD, division arose between the EOC and the OOC over the nature of the union between human & Divine in Jesus Christ.
The EOC position, of "dyophysitism"
(dyo-physis = two-natures), states that Jesus Christ is "two natures
[dyo-physis] in one person
[prosopon]". The Greek word for "person"
[prosopon] literally means "before the eyes" and refers to the ancient emotionally-expressive face masks worn by actors on stage. I think it means "superficial external appearance" as viewed from the outside, what you see before your eyes,
prima facie. Accordingly,
Jesus Christ = human + Divine united showing "one game face" (as it were)
Jesus the man from Earth had one terrestrial human nature, which was exposed to Divine Presence via the Holy Spirit (generated by & proceeding) from God in heaven. Jesus the man "psychologically submitted" his human will to Divine Will, saying "not my will but Thy Will be done" (Luke 22:42, Lord's Prayer). Thus, human & Divine came to an "understanding" with Jesus' human nature aware of & consciously choosing to obey Divine Command, such that God in heaven told Jesus on Earth "what to say & how to say it" (John 12:49).
Now, others have tried to espouse "monophysitism"
[mono-physis = one nature], that Jesus' terrestrial human nature was obliterated by Divine Presence "as a drop of vinegar is dissolved in the ocean". According to that picture, Jesus became a "mindless lobotomized zombie" (so to speak) inhabited by a psychologically over-whelming Divine Will that "took over his body & drove it around". This doctrine was declared in error at the Council of Chalcedon in 451 AD.
If monophysitism were true, then (insofar as it applicable) how could the Patriarch Abraham have "negotiated with God" about the righteous inhabitants in Sodom (Gen 18)? That would suggest, rather, that Abraham's human nature "bravely questioned" Divine Presence until they reached a new "understanding" (spare the city on account of ten righteous individuals).
Likewise, Mary consciously submitted her human nature & will to Divine Will, "Thy Will be done". Indeed, all Christians recite the Lord's Prayer, "Thy Will be done". But Christians do not generally claim that their human natures are obliterated and "dissolved like drops of vinegar in the ocean". Rather, their natural human will consciously submits to Divine Will, "Thy Will be done".
So, I think that Christians have been maintaining a consistent "dyophysite story" (so to speak) since the days of Abraham around four thousand years ago. Divine Will from God in heaven does not "obliterate" natural human conscious will, but rather seeks its willing submission to Divine Will & Divine Command.
The "monophysite error" (according to Chalcedon) sounds more like Demonic Possession, wherein the natural human conscious will is (according to descriptions) more powerfully
suppressed. But even there, after Jesus & the Apostles cast out the Demonic Spirits, the humans reverted to their right minds & good ol' selves, again suggesting that the human nature is not "dissolved away".
In sum, per the original quote of Luke 1:38, I think that the only Christian-consistent claim is that
Mary's natural human will was involved in consciously deciding to submit to Divine Will. That created a "harmonious understanding" paving the way for the birth, maturation, and ministry of Jesus Christ.