I’m talking about the Vulgate in 1592 after the Council of Trent. The Clementine Vulgate. They include the Prayer of Manasseh and 3 and 4 Esdras in an appendix.
Clement Vlll said in the preface
Oratio Manassa, necnon Libri duo, qui sub libri Tertii & Quarti Esdrae nomine circumferuntur, hoc in loco, extra scilicet seriem canonicorum Librorum, quos sancta Tridentina Synodus suscepit, & pro Canonicis suscipiendos decreuit, sepositi sunt, ne prorsus interirent, quippe qui a nonnullis sanctis Patribus interdum citantur, & in aliquibus Bibliis Latinis tam manuscriptis quam impressis reperiuntur.
The Prayer of Manasseh, as well as two books, which circulate under the name of the Third and Fourth Book of Ezra, are set aside in this place—that is, outside the series of canonical books, which the holy Tridentine Synod accepted, and determined should be taken up for canonical—lest they should perish completely, since they are sometimes cited by some of the holy Fathers, and they are found in some Latin books, both manuscript and printed.
So the Church always promoted Catholics reading them even if they weren’t considered canonical scripture.