Personally I am not a big fan of it… I have been engaged to be married twice. I believe that it should be seen as in this use of the word

engagement – a hostile meeting of opposing military forces in the course of a war; “Grant won a decisive victory in the battle of Chickamauga”; “he lost his romantic ideas about war when he got into a real engagement”

It can of course also be seen to mean

1. The act of engaging or the state of being engaged.

2. Betrothal.

3. Something that serves to engage; a pledge.

4. A promise or agreement to be at a particular place at a particular time.

5.

a. Employment, especially for a specified time.

b. A specific, often limited, period of employment.

6. A hostile encounter; a battle.

7. The condition of being in gear.

Synonyms: engagement, appointment, assignation, date¹, rendezvous, tryst

Anyway, I am very happy for the both of you! You deserve the happiness I see between you two.