Was Hebrews included in the canon solely because it was assumed to be authored by Paul, or was there any other basis for its canonization?
From Eusebius' Canons, one of the earliest church histories (early 300s AD) we have:
Paul’s fourteen epistles are well known and undisputed.593 It is not indeed right to overlook the fact that some have rejected the Epistle to the Hebrews,594 saying that it is dis puted by the church of Rome, on the ground that it was not written by Paul. But what has been said concerning this epistle by those who lived before our time I shall quote in the proper place.596 In regard to the so-called Acts of Paul,597 I have not found them among the undisputed writings.598
Interestingly, Eusebius' view is not really accepted anymore in this regard, but he also rejects 2 Peter, so its not like he's infallible. As Phillip Schaff (the editor of the Ante-Nicene Fathers, from whom this is taken, explains as follows:
τινες ἠθετήκασι. That the Epistle to the Hebrews was not written by Paul is now commonly acknowledged, and may be regarded as absolutely certain. It does not itself lay any claim to Pauline authorship; its theology and style are both non-Pauline; and finally, external testimony is strongly against its direct connection with Paul.