Well, knowing about “Donation of Constantine” and the fact that there was a legend about Constantine baptized by Pope Sylvester I is a clue that shows the general ignorance about the circumstances of Constantine’s baptism (few days before his dead). Or perhaps an imposible attempt to justify or legalize an “authentic” (catholic) baptism rather a false (heretic) one.
But the unquestionable fact is when Eusebius of Nicomedia baptized Constatine (337 a.D.) he wasn’t in good standing with Catholic Church. He (by plots against key bishops of the Nicean Council, who defended catholic trinitarian and nicean doctrine) was the responsible of the exile of Eustathius of Antioch (330), Athanasius of Alexandria (335) and Marcellus of Ancyra (336). All of them years before baptism of Constantine (337).
Paulinists and arians denied the divinity of Christ like JW today. All of them baptize with the trinitarian formula. Is JW baptism valid?
And of course Athanasius of Alexandria denied validity to arian baptism
documentacatholicaomnia.eu/03d/0295-0373,_Athanasius,Orationes_contra_Arianos%5BSchaff%5D,_EN.pdf
Read specially paragraphs 41-42-43 (page 784)
For where the Father is, there is the Son, and where the light, there the radiance; and as what the Father worketh, He worketh through the Son2477, and the Lord Himself says, ‘What I see the Father do, that do I also;’ so also when baptism is given, whom the Father baptizes, him the Son baptizes; and whom the Son baptizes, he is consecrated in the Holy Ghost. And again as when the sun shines, one might say that the radiance illuminates, for the light is one and indivisible, nor can be detached, so where the Father is or is named, there plainly is the Son also; and is the Father named in Baptism? then must the Son be named with Him.
…]
“I mean Baptism; for if the consecration is given to us into the Name of Father and Son, and they do not confess a true Father, because they deny what is from Him and like His Essence, and deny also the true Son, and name another of their own framing as created out of nothing, is not the rite administered by them altogether empty and unprofitable, making a show, but in reality being no help towards religion? For the Arians do not baptize into Father and Son, but into Creator and creature, and into Maker and work . And as a creature is other than the Son, so the Baptism, which is supposed to be given by them, is other than the truth, though they pretend to name the Name of the Father and the Son, because of the words of Scripture, For not he who simply says, ‘O Lord,’ gives Baptism; but he who with the Name has also the right faith . On this account therefore our Saviour also did not simply command to baptize, but first says, ‘Teach;’ then thus: ‘Baptize into the Name of Father, and Son, and Holy Ghost;’ that the right faith might follow upon learning, and together with faith might come the consecration of Baptism.”
Saludos