Does the term mitqaddešet (consecrated) mean "Engagement"? Seems to have this meaning in rabbinic literature bu not in the bible. According to Maimonides, Mishneh Torah, Sefer Nashim, Ishut 3,11 indicates the "betrothal" of a three-year-old girl and a day that occurs through "sexual intercourse" (the term is bǝbîʾâ) with the consent of the father, least from what Rabbi Eliyahu Touger translates into English "If a girl is older than three years and one day, she can be consecrated through sexual relations with her father's consent". Confirm the translation of the term consecrated with Engagement? Shalom.
Miskudeshes means betrothed, literally consecrated or set aside / made holy. It could occur via intercourse (see Mesechta Kiddushin, "Kesef, Shtar, Biah") but practically never does.
It's usually via the two other means. Document (shtar), and value-exchange ("kessef") as via intercourse it's lewd and thus carries a makkos penalty.
As @PloniAlmoni noted, the usage of Mitkadeshet by the Rambam and in most other sources refers to the betrothal-marriage process. However, in the bible the root קדש (KDSh) could also refer to prostitution or depravity. For example, Beresheet 38:21:
וַיִּשְׁאַ֞ל אֶת־אַנְשֵׁ֤י מְקֹמָהּ֙ לֵאמֹ֔ר אַיֵּ֧ה הַקְּדֵשָׁ֛ה הִ֥וא בָעֵינַ֖יִם עַל־הַדָּ֑רֶךְ וַיֹּ֣אמְר֔וּ לֹא־הָיְתָ֥ה בָזֶ֖ה קְדֵשָֽׁה׃
"He inquired of the people of that town, “Where is the cult prostitute, the one at Enaim, by the road?” But they said, “There has been no prostitute here.”
In the Hebrew, Tamar, who had dressed up like a prostitute, is called by Chirah the Adulamite a "kedesha" which means "prostitute".
Side-note: It's possible that the term comes from Qetesh/Qedesh, the Canaanite deity of fertility, ecstasy and pleasure.