You ask about “a close examination of the Hebrew involved in Isaiah’s [11:1] prophetic expression”.
All right. The Hebrew text is the following:
ויצא חטר מגזע ישׁי ונצר משׁרשׁיו יפרה
“And there shall come forth a shoot out of the stock of Jesse, and a twig shall grow forth out of his roots.” (JPS)
First of all - in MT - the term נצר (as noun, which you transliterate netser) occurs 3 times (not “one single time”, as you say): Isa 11:1, 14:19, and Dan 11:7.
From the phraseology used by Isaiah (I will indicate with the symbol ‘>’ the consistent wording from JPS translation mentioned above), we may conclude that – in addition to his usage of MT roots as שׁרשׁ (‘to be radicated’ > “roots”), גזע (‘to be truncated’ > “stock”), and פרה (‘to be fruitful’ > “grow forth”) - he utilized 3 variants of the same conceptual root, possessing the meaning of ‘to come out, to sprout up’. The three variants showed in the verse are: יצא (> “come forth”), חטר (> “shoot”), and נצר (> “twig”).
Not every Bible student know that a common linguistic (all tongues, Hebrew included) trend (although not desirable) is that a language gradually loses some of its original stringent structures (1) to embrace some more ‘simpler’ ones, or (2) to ‘leaving around’ dialectal variations of some original terms.
In this specific case, Isaiah, made use of a linguistic redundance, not only utilizing a synonimic parallelism (that is a form of didactical redundance, too), but also mentioning the same concept (‘to come out, to sprout up’) through 3 allographic (it means “with a different graphic [form]”) variants. This fact did not must appear odd. There are hundreds occurrences of this phenomenon, in MT.
Since this site isn’t a linguistics-specialized one, I avoid here to expand the matter on this point in the measure it deserves. So, I confine myself to mention only an underrated linguistic fact - yet ascertained in the past - to back the argument I’m exposing.
Shlomo ben Yitzschak of Troyes, commonly known as Rashi, commenting Lev 19:16, wrote: “Therefore, I say that the expression רָכִיל is an expression of ‘going around and spying מְרַגֵּל,’ whereby [the letter] כ [of the word רָכִיל] is interchanged with [the letter] ג [so that the word רָכִיל is equivalent to רָגִיל]. For all letters which stem from the same source are interchangeable with one another [i.e., letters by the same speech organs, namely, the lips, tongue, teeth, palate, or throat]. [For example], [the letter] ב [is interchangeable] with פ or ו [as they are all labials; the letter] ג [is interchangeable] with כ as is [the letter] ק [since they are all palatals; the letter] נ [is interchangeable] with ל [because they are both linguals, and [the letters] ר and ז [are interchangeable] with צ [as they are all dentals].” [https://www.chabad.org/library/bible_cdo/aid/9920/showrashi/true]. (The same full knowledge of this linguistic phenomenon was one of the grounds of the [Jakob] Grimm’s ‘Law’ [although – in this case - envisaging the sole Germanic languages]. Anyway, since the physiological man’s speech organs are the same for all people – in every epochs – it is no surprise that we are able to observe this phenomenon in almost every language of the world, ancient and contemporary)
In other words, a common linguistic trend is that - in a number of times - subsequent speakers (of a date language) prefer to utilize forms of a word that include consonantal commutations, compared to the original term.
Getting back to the point - Isa 11:1 - we have three terms [יצא (> “come forth”), חטר (> “shoot”), and נצר (> “twig”)] belonging to the same semantic area (‘to come out, to sprout up’). So, if now we apply the ‘Law’ of Rashi we may conclude that – through the commutations ח <> נ , and ט <>צ – we may argue that חטר (> “shoot”) and נצר (> “twig”) are two variants of the same word (the verbal form יצא [> “come forth”] also is graphically related to the others terms, but only through the medial radical [צ], since the other graphemes [י, andא] are negligible – in this case - as regards the basic meaning, aging them here as matres lectionis). Also Luis Alonso Schökel in his Diccionario Biblico Hebreo-Español equalizes חטר and נצר, including both in the same lemma.
But, if this being the case, why did Isaiah choose to utilize a number of allographic variants of the same word, instead to use a unique term?
The Rashi’s dissertation mentioned above demonstrates that inside the lexicon of the Hebrew Scriptures we find these graphical (not semantic) differences. A classical example of this phenomenon is described in Judges 12:4-6, when a linguistic commutation – developed by thousands of Ephraimites’ warriors - did cost their life. In this case, the tribe of Ephraim developed a commutated wording of a common term, that is, סבלת (SBLT) instead of שבלת (ŠBLT), commutating a shin (ש) into a samekh (ס).
John Gill (Exposition of the Bible) wrote (ad locum, bold is mine): “and he said, sibboleth; pronouncing the letter ‘shin’ as if it was ‘sin’, or a ‘samech’; just as the French, as Kimchi observes, pronounce ‘s’ like a ‘t’; and though the Gileadites and Ephraimites were of the same nation of Israel, and spoke the same language, yet their pronunciation differed, as did that of the Galilean Jews from others in the times of Christ, Mat 26:73, and so in all nations, among the Greeks, Romans, and among ourselves, people in different counties pronounce in a different manner; which Kimchi thinks was in the Ephraimites owing to the air or climate, as the French, he observes, pronounce ‘s’ as a ‘t’, with a soft and gentle sound.”
Jamieson-Fausset-Brown’s Commentary (ad locum, bold is mine): “The Eastern tribe had, it seems, a dialectical provincialism in the sound of Shibboleth; and the Ephraimites could not bring their organs to pronounce it.”
NET Bible note (ad locum, bold is mine): “The inability of the Ephraimites to pronounce the word shibboleth the way the Gileadites did served as an identifying test. It illustrates that during this period there were differences in pronunciation between the tribes.”
These data help us to conclude that the Isaiah’s usage of allographic variants was an useful device to be understood by all the tribes of Israel (including Judah [3:1-15; chapter 7; 9:21], Zebulun [9:1], Naphtali [9:1], Ephraim [9:21], Manasseh [9:21]), any regional (dialectal) variations of Hebrew language they spoke.
Sorry, but as far as I know, there’s (here in Isa 11:1) no different “aspects of ministry being conveyed of the one who is promised, being Messiah, the Christ”, as you say.
Anyway, this verse explain us how the Messiah had his origin in Judah’s tribe, and of the family of Jesse (Luk 3:31, 32), surely. This fact strenghten the faith of christians about Jesus of Nazareth as the true promised Christ of God.