And a recent one at that. One can find prayer books from Ukraine in even the late 1800s prior to the Synod of L'viv that do not include even a mention of "Supplikatisa".
Article 7 of the Union of Brest states
7.—That we should not be compelled to take part in processions on the day of Corpus Christi—that we should not have to make such processions with our Mysteries inasmuch as our use of the Mysteries is different.
While this article specifically refers to Corpus Christi, the last statement "inasmuch as our use of the Mysteries is different" most definitely applies here by extension. We can take this to mean that similar neolatinizations involving non-traditional usage of the Mysteries should also be treated in the same way (and indeed the hierarchs and the Synod take that opinion).
Praying before the Holy Altar in silence is certainly a praiseworthy thing as the Sisters do. Making it a liturgical thing out of concordance with the authentic received tradition is something entirely different.
In accordance with Article 7 of the Union of Brest (as well as the Instruction
, the directions of our Synod, the last Council of the Church, etc.) we of the UGCC should not be making use of this sort of liturgical neo-latinization that most certainly is not a traditional part of the Kyivan liturgical corpus outside of the Divine Liturgy or the giving of Holy Communion outside of the Liturgy.
I have in my hands as I write this (I wanted to check first-hand) the first Ukrainian Greek Catholic prayerbook specifically written in L'viv for the new Eparchy in the US by Fr. Lev Sembratovich and carrying the imprimatur of +Soter of Philadelphia of blessed memory in 1908.
It does not call it "Benediction" or "Supplikatsia" but simply "Prayers before the Holy Gifts", makes no mention of rubrics for a monastrance or elevation of a chalice or anything. Instead these prayers are included basically as a small appendix appearing after such occasional offices as the Paraklesis/Moleben to the Mother of God (which by the way in this book includes the full Canon of Supplication), Akathists to the Savior, the Mother of God, and St. Nicholas.
As a more general side note, I and many others here prefer to be referred to as a "Ukrainian Greek Catholic" or "Ukrainian Catholic" rather than a "Ukrainian Byzantine Catholic Rite" or "Byzantine Rite Catholic". We are a particular Church and not a "Rite".