I don't believe that's the proper understanding of "authentically" in that passage. It would seem to mean teaching by their authority as bishops:
For bishops are preachers of the faith, who lead new disciples to Christ, and they are authentic teachers, that is, teachers endowed with the authority of Christ, who preach to the people committed to them the faith they must believe and put into practice, and by the light of the Holy Spirit illustrate that faith. (Lumen Gentium §25)
Obviously some doctrine definitively taught by the entire episcopate would be consistent with the deposit of faith, for that is exactly what the infallibility granted to them guarantees! Otherwise this infallibility would be ridiculous: "they are infallible unless they are wrong".
Secondly, see the word "definitions"? That would be the declare, define, profess stuff. Dogmatic definitions are something very specific.
No, the "declare, define, profess" isn't necessary for a definition. This is clearly taught by Pope Pius XII in his encyclical Humani Generis:
22. To return, however, to the new opinions mentioned above, a number of things are proposed or suggested by some even against the divine authorship of Sacred Scripture. For some go so far as to pervert the sense of the Vatican Council's definition that God is the author of Holy Scripture, and they put forward again the opinion, already often condemned, which asserts that immunity from error extends only to those parts of the Bible that treat of God or of moral and religious matters. (§22)
In this case, he refers to the following text:
7. These books the Church holds to be sacred and canonical not because she subsequently approved them by her authority after they had been composed by unaided human skill, nor simply because they contain revelation without error, but because, being written under the inspiration of the Holy Spirit, they have God as their author, and were as such committed to the Church. (Dei Filius Ch. 2)
This is a definition which lacks the standard "declare/define/profess/teaches" formula, but is definitive by virtue of the intent to settle any further discussion on the issue, as is explained in LG 25:
And this is the infallibility which the Roman Pontiff, the head of the college of bishops, enjoys in virtue of his office, when, as the supreme shepherd and teacher of all the faithful, who confirms his brethren in their faith,(166) by a definitive act he proclaims a doctrine of faith or morals.(42*)
All that is necessary is that the teaching is clearly intended to be the "last word" on the issue.
Vatican II doesn't have any of that stuff.
As I have pointed out, the passage in Lumen Gentium §21 settles the issue of the sacramentality of episcopal ordination, which was still a disputed issue before the Council. The formula "the Sacred Council teaches", combined with the intent to "declare and proclaim before all men the doctrine concerning bishops" and Paul VI's intention that the Third Session settle the issue with "a certainty which may not be called into doubt" clearly makes this a definition. This is made more evident by the use of "teaches", which has been used in solemn definitions by other councils:
It firmly believes, professes, and teaches that no one conceived of man and woman was ever freed of the domination of the Devil, except through the merit of the mediator between God and men, our Lord Jesus Christ; He who was conceived without sin, was born and died, through His death alone laid low the enemy of the human race by destroying our sins, and opened the entrance to the kingdom of heaven, which the first man by his own sin had lost with all succession; and that He would come sometime, all the sacred rites of the Old Testament, sacrifices, sacraments, and ceremonies disclosed. (Council of Florence, Cantate Domino)
Dei Verbum §9, which settles the question of whether Sacred Tradition and Holy Scripture are from one or two sources, is probably a definition, as "following in the footsteps of the Council of Trent and of the First Vatican Council, this present council wishes to set forth authentic doctrine on divine revelation and how it is handed on" (§1).