In the Reformed tradition, the teaching of Isaiah chapter 11 IS taught, but because the seven gifts listed apply to the Messiah, a distinction is seen between that passage, and the gifts of the Spirit that Christians may receive, as in Rom. ch. 12, 1 Cor. ch. 12 and Eph. ch. 4. Care needs to be taken not to so inflate a Christian with ideas about the fruit of the indwelling Spirit's gifts that he or she begins to think prophecy that applies to Christ should also apply to them. Your helpful quotes from the Catholic perspective on Isaiah ch. 11 show that this passage is being applied to individual [Catholic?] believers (no doubt having first acknowledged application to Christ).
Examples of Reformed care are shown here, in two Reformed writings. I cannot date the first book as I only have the 27th edition of the original. The writer of the Introduction (Dr. R.A. Torrey) had come across the original 20 years earlier, but there is no date for either.
"Isaiah XI The peaceable kingdom of the Branch out of the root of
Jesse, vss. 1-9. Vs. 1, And there shall. The prophet having
described the destruction of the Assyrian army under that of a mighty
forest, here takes occasion to represent the GREAT PERSON, who makes
the subject of this chapter, as a slender twig... Vs. 2, the Spirit
of... [lists many related scripture texts, but none that speak of
Christians having gifts of the Spirit] Vs. 3, shall make him [and
through to vs. 9, speaks only of 'Him' being the object of these gifts
of the Spirit.] The Treasury of Scripture Knowledge from Canne,
Browne, Blayney, Scott & others; pp. 436-7. Bagster London, Revell New
Jersey (Capitals the author's.) [See my footnote.]
Of note, it goes on to link striking the earth with "the rod of his mouth" (vs. 4) with Revelation 1:16, 2:16 & 19:15 where the risen Christ is individually identified with this action: "...and out of his mouth went a sharp two-edged sword ...with it he should smite the nations". Again, no related scripture references point to Christians.
Another point that is found in the Reformed tradition is speaking of spiritual gifts that may appear in individuals who yet lack the grace of God - which never could be said of Christ! Consider:
"Still farther may an individual go in an approximation to the
evidences of true godliness, and yet remain unregenerate. He may
possess eminent spiritual gifts - fluency of expression in prayer -
great exhortatory powers - eloquence in preaching - clear
discrimination in spiritual subjects - the discerning of spirits - the
gift of speaking and of interpreting of tongues; yet continue a
graceless soul, retaining the 'carnal mind' and the 'heart of stone.'
What, we ask, is the most instructive and solemn page in the history
of the Corinthian church? - that which teaches us that great gifts
may exist in union with great impiety; in other words, that gifts are
not graces, that an individual, or a community of individuals, may
possess the gifts that edify, and at the same time be destitute of the
grace that humbles and sanctifies." The Work of the Holy Spirit,
p.40, Octavius Winslow, 1961 reprint. The original was published in
1891 with the title, Personal Declension and Revival of Religion in
the Soul. (Emphases the author's.)
My answer avoids all reference to modern views about spiritual gifts, such as in Pentecostal, Charismatic and Alpha Course circles. But in the Reformed tradition, I would suggest that the difference between that view of Isaiah ch. 11 vss 1-9 and the Catholic view is mainly due to keeping a clear distinction between the role of the Holy Spirit in Christ as the individual, the Messiah, "full of grace and truth" (John 1:14) and the fruit of the Holy Spirit's gifts in believers in Christ. There may be much more to it than that, of course.
As to your question about moving away from St. Augustine's stance on this point, I would just quote your statement, "Between the 11th and 13th centuries medieval theologians explored the connection between the Holy spirit gifts and the virtues until the theology of the gifts and virtues were settled with St. Thomas Aquinas's theology." Therein lies the answer. The Reformed tradition found much in Augustine's writings with which to agree, but by the 11th century they found much medieval theology with which to disagree. It also goes without saying that just because one finds much to agree with in Augustine, is not to say that one will therefore agree with everything! Nor must all the links and interpretations of later scholars of necessity be bound to follow.
My answer would end with the words of Christ on this matter. In Luke ch. 4, Christ read from another portion of Isaiah (ch. 61), saying at the end of his synagogue reading, "This day this scripture is fulfilled in your ears". Isaiah, as we know contains many prophecies about Messiah, all of which were fulfilled in Christ. His relationship with the Holy Spirit is unique, as all Isaiah's prophecies about Messiah show. Reformed Christians may be keen to avoid applying to themselves what uniquely applies to Christ, as that would be presumptuous.
EDIT: Further to comments, I checked Calvin's Commentary on Isaiah. The only bit Calvin wrote on Isa. 11:1-3 that is connected to your question is:
“Hence we infer that this prediction applies solely to the person of
Christ; … The Spirit of the Lord We must keep in view what I mentioned
a little ago, that this refers to Christ's human nature; because he
could not be enriched with the gift and grace of the Father, except so
far as he became man. Besides, as he came down to us, so he received
the gifts of the Spirit, that he might bestow them upon us. And this
is the anointing from which he receives the name of Christ, which he
imparts to us; for why are we called Christians, but because he admits
us to his fellowship, by distributing to us out of his fullness
according to the measure (Ephesians 4:7) of undeserved liberality? And
undoubtedly this passage does not so much as teach us what Christ is
in himself, as what he received from the Father, that he might enrich
us with his wealth…”
The Prophet does not here enumerate all the gifts of the Holy Spirit,
as some have thought. Out of this passage the Papists have foolishly
and ignorantly drawn their sevenfold grace, and some of the ancients
fell into a similar blunder. He enumerates only six kinds; but they
have added a seventh out of their own head. But as one error commonly
follows another, they have chosen to limit the gifts of the Spirit to
the number seven, although in other parts of Scripture (John 14:17; 2
Timothy 1:7) he receives numerous and lofty commendations drawn from
the variety of the effects which he produces. Besides, it is very
evident that it is through the kindness of Christ (Galatians 5:22, 23)
that we are partakers of other blessings than those which are here
enumerated, of meekness, chastity, sobriety, truth, and holiness; for
these proceed from none else than from Christ. He does not mention,
therefore, all the gifts which were bestowed on Christ, for that was
unnecessary; but only shows briefly that Christ came not empty-handed,
but well supplied with all gifts, that he might enrich us with them.
If these things had not been added, we might have supposed, as the
Jews commonly do, that the restoration of this kingdom was carnal, and
might have imagined that Christ was poor and destitute of all
blessings. Accordingly, the Prophet afterwards shows that the gifts of
the Spirit are laid up in him, first, generally, and next,
particularly; that we may go to him to obtain whatever we want. He
will enlighten us with the light of wisdom and understanding, will
impart to us counsel in difficulties, will make us strong and
courageous in battles, will bestow on us the true fear of God, that
is, godliness, and, in a word, will communicate to us all that is
necessary for our life and salvation. All gifts are here included by
the Prophet, so that it is excessively foolish to attempt to conceal
those which do not belong to the present enumeration."
Footnote: R.A. Torrey is not ‘Reformed’ but is a Pentecostal believer who teaches that there are seven easy steps to receiving Holy Spirit baptism. He may comment on Isaiah ch. 11 in his book The Holy Spirit: Who He Is and What He Does, as he has two chapters on those seven steps – I don’t know. But he is not in the Reformed tradition. Also, I searched the commentary on Isaiah ch. 11 in a Reformed writer’s book of 300+ years ago – Matthew Henry – but he says not a word about any link with NT gifts of the Spirit. He applies the first 9 verses entirely and uniquely to Christ.