The Old Testament and the New Testament are different sections of the library. To think of this division as "insert a title page" is too far off the mark.
Imagine, if you will, a library of 66 books, written over the course of 1500 years, by 40 different men (possibly one woman). As each of these works was created, it doesn't make sense to ask "When did someone insert a title page?" Rather, each work was created individually, and had its own distinction.
Eventually, these 66 (or 73 if you are Catholic) were recognized as the "best of the best." And, as such, these became the manuscripts to have in your collection. Over time, the Jews assembled the 39 manuscripts known as the "Old Testament" and even dictated the order in which they should be shelved on the library. (The 12 minor prophets, for example, have a keyword at the end of each book that corresponds to the keyword at the beginning of the next.) An additional 7 books were considered the best runners up, and shelved accordingly.
By around 400 BC or 200 BC, the "Old Testament" was pretty well decided, and fixed.
In the First century after Christ, however, his work was so important to Christians that the apostolic writers' works were seen as being as important, if not moreso, to Christians then the original Jewish Scriptures. While each of the works in question (Gospels, histories, letters from Paul, Peter, and James) was written between about 50 AD and 100 AD, they were, over time, also selected as the best of the best.
In order to distinguish the two origins - one distinctly Jewish, one Christian - they were shelved in different places - Old Testament and New.
With the invention of the printing press in 1453, it became affordable for people to have all of these manuscripts. In order to save on printing costs, all 66 - 73 books were eventually printed under one binding. The canonical order of the books was set by tradition, and the contents were already in agreement. In order to help people locate the books, they were separated into the two categories.
As such, the technical answer to your question is - Gutenberg is responsible for the "Title Page," but all he was doing was following history and convention. These separate books had been separate all along.
Note: The 'title page' you show is just a restatement of a creed:
ὁ παλαιᾶϲ καὶ καινῆϲ διαθήκηϲ θϲ
Oh God of the old and new covenant
ὁ ἐν τριάδι ὑμνούμενοϲ
who in trinity is praised
καὶ ἐν μονάδι δοξολογούμενοϲ αὐτὸϲ
and in unity is glorified:
δέξαι τὴν μετάνοιαν τοῦ ἁμαρτωλοῦ θεοφυλάκτου
receive the repentance of a God-guarded* sinner
καὶ ἀξίωϲον αὐτὸν τυχεῖν τῆϲ βαϲιλείαϲ ϲου
and count him worthy to attain your kingdom
διὰ ϲπλάχνα ἐλέουϲ ϲου
by the bowels of your mercy
καὶ ἐλέοϲ ἀμέτρητον
yea mercy immeasurable.
It should be noted that Codex Sinaiticus is the oldest Greek Manuscript we have - but it is just that - a codex. (Tischendorf found these manuscripts in a trash can in the monastery at Sinai and
stole brought them back to England. It's the oldest manuscript we have. What you are linking to are copies of each of the bound manuscripts.)
*Possibly the scribe's name: "this sinner, Theophylact".