I would say in this case, the plural form is just a Hebraicism and has no theological significance.
The Hebrew word for heaven is "shamayim" which has the ending of a dual form, related to "mayim" or "waters". This is a very old morphological form and does not mean that there are two of them anymore than there are two "waters".
Indeed the heavens above are separated from the waters below as described in Gen 1.1, reflecting the commonly held ancient near east view of the earth as being a square with water above and below.
All 99 places where "heaven(s)" appears in the Old Testament are always "shamayim" in Hebrew and are always the plural (dual) form. How they are translated depends on whatever sounds better to the reader's ear. There is no mention of a "first" or "second" heaven in the Old Testament.
By the way, you see the same issue with "mayim" or "waters" which are sometimes translated in singular or plural but are always the plural (dual) form in Hebrew. See, for example Is. 3.1 and Is. 1.22 where the same surface text Hebrew is translated differently based on whatever reads better in the view of the translator. We shouldn't develop a theology of the "first" and "second" water based on the fact that mayim is sometimes translated as singular and sometimes as plural.
The idea of different heavens dates to the apocalyptic literature starting in the late intertestamental period on, such as 2 Enoch. Here is the NICNT:
There is some debate as to the number of heavens currently believed
in; some sources suggest five, others ten, though seven heavens are
referred to in both Jewish and later Christian writings (Apoc. Moses
35:2; 2 Enoch 3–20; Ascension of Isaiah 3:11; Apoc. Paul 29. See
further C. Rowland, Open Heaven, 381). For two reasons, however, Paul
is thinking here of the highest heaven: (1) the preposition ἕως
implies “up to,” “the ultimate,” and (2) the supernal connotations of
“Paradise” (v. 4), which is a synonym for “third heaven.”
Barnett, P. (1997). The Second Epistle to the Corinthians. Grand Rapids, MI: Wm. B. Eerdmans Publishing Co.
This is also the period in which angels were named and elaborated upon (e.g. "Metatron") and there was a lot of interest in metaphysics, but influenced by Hellenism, there was a new desire to categorize and describe the structure of the spiritual realm, how it operated, who ran it, the various orders and ranks of spiritual beings, etc -- in a way very foreign to the Old Testament.
So definitely by the time of the New Testament, there was a popular acceptance of more than a single heaven, but seeing as how the Hebrew word was always plural (technically, dual), unless you see "first" or "second" in front of "heaven(s)", relying on the plural form to infer that it is a "first" or "second" heaven is unsound, especially when reading Greek accounts written by Jews of discussions that happened in Hebrew/Aramaic - and this explains why translations often ignore the singular or plural form and choose to use "heavens" as a synonym for "heaven" based on whichever sounds better to the reader's ear.