Jesus would not have used written Targums--they didn't exist yet.
"The Targums" are translations of the Hebrew scriptures into Aramaic. While oral translations into Aramaic were permitted in the second-temple period, written translations into Aramaic were not. This did not come about until after AD 70.
From New Testament scholar and linguist Claude Tresmontant:
There were oral translations in Aramaic of the sacred books written in Hebrew; they were called targumin. A translator in the synagogue would read aloud, translating a passage from the Torah or one of the prophets. But in the era before the destruction of the Temple, putting these translations into writing was formally prohibited. (The Hebrew Christ p. 5)
The scrolls in the synagogues in Galilee would have been Hebrew documents. There is evidence of at least one Greek-speaking synagogue in Judea (in addition to the more prevalent Hebrew), meaning the Septuagint (the Greek translation of the Hebrew scriptures) would have been familiar to at least some of the populace in the region, but the predominant language of the local synagogues in Jesus' day was Hebrew.
When John refers to "the scriptures", this is a reference to the Hebrew Bible in the Hebrew language. While it was commonplace a century ago to argue that Hebrew was a dead language by the first century, the discovery of the Dead Sea Scrolls overturned the evidence upon which this theory rested. Hebrew changed over the centuries (as all languages do), but Hebrew was alive and well (written & spoken) in Jesus' day.
Perhaps the plainest (and admittedly ever-so-slightly over-simplified) rendering of the trilingual nature of Jesus' world I have encountered is that Aramaic was the language of the home, Hebrew was the language of the synagogue, and Greek was the language of the marketplace.
Appendix 1--the trilingual world of ancient Galilee
For a more extensive discussion of the trilingual world in which Jesus was raised, see this video on my channel: What languages did Jesus speak?.
For evidence that ἑβραϊστί in the New Testament is a reference to Hebrew, not to Aramaic, see Buth & Pierce's work: Hebraisti in Ancient Texts: Does ἑβραϊστί Ever Mean 'Aramaic'?.
For a review of the political (and anti-Semitic) reasons for which 19th-century German scholars tried to convince the world that Jesus did not speak Hebrew, see Baltes' work here.
Appendix 2--dead languages
What is a dead language? Oxford Languages defines it as:
a language which is no longer in everyday spoken use, such as Latin
When scholars have claimed that Hebrew was a dead language in the first century, what did they mean?
The following arguments were made prior to the discovery of the Dead Sea Scrolls:
Thus, the knowledge of Hebrew among the common people, unless they
were learned scribes . . . was limited to the memorization of a few phrases,
prayers and psalms. The rest of his private, public and religious communication would have been in Aramaic (Arnold Meyer, Jesu Muttersprache. Das galiläische Aramäisch in seiner Bedeutung für die
Erklärung der Reden Jesu pp. 46-47. Published 1896)
As the proof has been offered with comparative frequency of late that the ‘Hebraists’, i.e. the ‘Hebrew’-speaking Jews of Palestine . . . did not in reality speak Hebrew but Aramaic, it seems superfluous to raise a fresh discussion in all the details of this question (Gustaf Dalman, Die Worte Jesu: mit Berücksichtigung des nachkanonischen jüdischen
Schrifttums und der aramäischen Sprache erörtert, published 1898)
Guido Baltes offers the following, up-to-date (and in particular, post-Dead Sea Scrolls discovery) response:
Dalman assumed that the only raison d’être for a targumic practice was the necessity of translation because no one understood Hebrew. However, more recent studies into the character and function of the targum suggest that commentary
was as important as translation as a functional aspect of targum, especially in the “Palestinian” type. The existence of targum therefore does not necessarily imply a lack of Hebrew language competence, but the desire to expound the
meanings of the Hebrew text without having to alter or expand it (p.18 here)
A century ago, heavily influenced by scholars such as Pfannkuche, Meyer, Zahn, and Dalman (ibid), it was believed that Hebrew was in the time of Jesus essentially as dead as Latin is today--it was a language that existed only in academia.
Various evidences contradict this older scholarship, most notably the Dead Sea Scrolls, which show that in Qumran people were not only copying existing Hebrew writings, but producing novel Hebrew writings & actively communicating with one another in Hebrew.
Further distinction between Biblical Hebrew & Mishnaic Hebrew may be a valuable topic for discussion for a separate question. Suffice it to say that the Hebrew of the first century had been influenced by Aramaic (and other languages), and was not identical to the Hebrew of Isaiah.
The same could be said in comparing 21st century English to Elizabethan English. Elizabethan English is not "dead" in the sense that Latin is. It is not spoken colloquially, but highly influential works (e.g. Shakespeare, the King James Bible) in Elizabethan English have sustained active use of Elizabethan English in churches, theaters, and other locations outside academia.
- Was Biblical Hebrew dead in the time of Jesus? It was about as dead as Elizabethan English is today (less dead than Latin is today).
- Was Hebrew dead in the time of Jesus? No. The Hebrew spoken at the time of Jesus was closer to what we would call Mishnaic Hebrew than Biblical Hebrew, and it was alive. Its contemporary use is evidenced by the Dead Sea Scrolls, coins, Josephus, Talmudic parables, etc. See further discussion on this site by Frank Luke here.