Pius XII Humani Generis
27. Some say they are not bound by the doctrine, explained in Our Encyclical Letter of a few years ago, and based on the Sources of Revelation, which teaches that the Mystical Body of Christ and the Roman Catholic Church are one and the same thing.[6] Some reduce to a meaningless formula the necessity of belonging to the true Church in order to gain eternal salvation. Others finally belittle the reasonable character of the credibility of Christian faith.
I could post more but have to do a little work at the moment
Sure, the Church is (not Christ) but the Mystical Body of Christ. That's undisputed.
The encyclical
Mystici corporis says that Christ is the Head and the Church is the Body. The Body does not include the Head. In #53 Pius says that "Christ in a certain sense lives in the Church, that she is, as it were, another Christ". But: not "the Church is Christ", rather "the Church is
another Christ". And this must be understood correctly:
54. Nevertheless this most noble title of the Church must not be so understood as if that ineffable bond by which the Son of God assumed a definite human nature belongs to the universal Church; but it consists in this, that our Savior shares prerogatives peculiarly His own with the Church in such a way that she may portray, in her whole life, both exterior and interior, a most faithful image of Christ. For in virtue of the juridical mission by which our Divine Redeemer sent His Apostles into the world, as He had been sent by the Father, it is He who through the Church baptizes, teaches, rules, looses, binds, offers, sacrifices.
Not "the Church is Christ", rather "the Church is a most faithful image of Christ".