I think that the language of "intended audience" is problematic, since "intentionality" begs a host of questions, and these have the potential to raise the emotional stakes quite quickly.
There is, however, other language for talking about the "levels" that OP signals, and my own sense is that any of these levels would be fair -- provided that questions and answers are commensurate. With that proviso in place, I would like to introduce language used by Walter Moberly that is very helpful, just at OP's point of interest (and with the closing comments in the "question" especially in mind).
In a number of publications, but prominently in his recent The Bible in a Disenchanted Age (Baker Academic, 2018), Moberly has refined his use of three readerly stances in relation to the biblical text (or any text from antiquity, for that matter), the 'the world behind, the world within, and the world in front of the text':
- ‘behind’ = ‘context of composition and initial use’ (The Bible in a Disenchanted Age, pp. 32, 66–7, etc.)
This approximates to ‘historical-critical’ readings, those informed judgments about how the text came to have its present shape, the historical forces of "production", if you like.
- ‘within’ = ‘narrative framework/setting’ (The Bible in a Disenchanted Age, pp. 32−3, 66–7, etc.)
This stance approximates to ‘canonical’/literary readings, or what we might think of as the world of the "implied narrator": the "surface level" of the text.
- ‘in front of’ = ‘those communities who have looked to, and in significant ways identified with, the content of these works as they read and appropriated them in contexts beyond their origins’ (The Bible in a Disenchanted Age, p. 110)
This approximates to ‘reception’, the interests and values informing readings by later communities, whether in an earlier period (e.g., medieval, or 'Victorian', etc.). or in our contemporary world, and whether from Jewish, Christian, secular, etc. perspective.
As Moberly elseswhere notes, this sort of language resists privileging any one of these (equally "valid") approaches, and yet provides clarity about what kind of discourse or "reading" is in mind.
He uses this language also in his earlier Old Testament Theology: Reading the Hebrew Bible as Christian Scripture (Baker Academic, 2013). Here is an extended passage (pp. 283-4) in which he explains its use. (I have taken the liberty of dividing up a fairly long paragraph--easier to read in print than "wall-of-text" on screen!):
It might help to pose the issue differently. In my discussions I have made use
of the conceptuality of the world within, the world behind, and the world in
front of the text. Almost all interpreters are interested, in one way or another,
in the world within the text. The question becomes how one contextualizes
this world within the text, which relates also to the nature of the imaginative
moves that are brought to bear upon it.
The dominant move in modern
biblical scholarship has been to relate the world within the text to the world
behind the text—to look backward, as it were, from the Old Testament to the
world that gave rise to it, the immediate world of Israel and also the wider
world of the ancient Near East. This means, for the most part, a focus on
times and places before ever there was an Old Testament, when at most there
were incipient collections and compilations of material that only over time
became Israel’s scriptures.
My approach, by contrast, has been to focus primarily
upon the world within the text in relation to the world in front of the
text—to look forward from Israel’s scriptures toward those enduring faiths,
both Jewish and Christian, that appropriate this material as Scripture and
understand themselves in relation to it. For this approach, Israel’s scriptures
as an authoritative collection are a given from the outset (and issues to do with these scriptures being received in Greek as well as Hebrew, and with disagreements
over the boundaries of the canon, make no significant difference to this basic stance).
In drawing this basic distinction of approach, there is no need to polarize
unnecessarily. Many scholars whose primary interest is the world behind the
text are still interested in facets of the world in front of the text. And in my
readings, although the world behind the text has been subordinated, it has not
been ignored; judgments about the nature and genre of the text and how best
to read it are informed by judgments about likely context and date of origin
(despite the great difﬁculties in being conﬁdent about such matters, given the
paucity of ﬁrm evidence).
If questioners and answerers on BH.SE were to use this kind of categorization (or something like it) with clarity and self-conciousness, I believe we would be able to make room for the sort of "levels" OP has in mind, without the "baggage" (and diatribe) that sometimes features in our Q&A's and their comment threads.