Hello, there's a lot to unpack here but I'll try my best. I answered a similar question to yours here that I hope will prove useful.

The answer, as with many cases, comes down to who you read. To Gildas, in his de Excidio Britanniæ, the Angles and Saxons were the wrath of God made manifest, a punishment called down upon the Romano-British for their decadence, greed and degeneracy, a sentiment later echoed by Bede, albeit with the slant that the English are, essentially, the tools of divine will:

In short, the fires kindled by the Pagans proved to be God's just punishment on the sins of the nation, just as the fires once kindled by the Chaldeans destroyed the walls and buildings of Jerusalem.

Bede doesn't shy away from the pagan and antagonistic origins of the English; after all, what better conversion narrative than to have the manifestation of divine judgement subsequently turn to the faith. Bede also prides himself on being historically thorough and honest, which does make it somewhat ironic that his invasion-and-replacement narrative has been fairly extensively disabused. Substantial archaeological evidence, toponyms, and even some literary evidence suggests a far more gradual and piecemeal conglomeration of Germanic settlement often overlapping or neighbouring rather than replacing British communities, with regional ethnic identities (e.g. all Mercians are Anglian, the Kingdom of the East Saxons) only really appearing as large-scale polities started emerging in the seventh century. Æthelberht of Kent, in his legal codex of c.597, for example, identifies just as Æthelberht cyning. The later codex of Hlothhere and Eadric identifies them as Cantwara cyningas - kings of Kent - identifying with the pre-Roman territory and the Cantiaci mentioned by Julius Caesar rather than the Jutish ethnicity prescribed to them by Bede. It's not until the late Seventh Century, with codices like that of Ine of Wessex, that you see definite identification such as Wesseaxna kyning - King of the West Saxons.

A similar narrative of divine retribution is certainly applied by later English writers to the Danes. Archbishop Wulfstan of York's famous Sermo Lupi ad Anglos, written at the peak of the Danish attacks of 1010-1016. The sermon is a furious admonition for the many sins and vices which Wulfstan sees as plaguing the English, and indeed Wulfstan actively references Gildas, implying that the Danes are a similar threat of divine wrath to that which the English themselves once were, and haranguing the English to avoid such a fate:

But let us do as is necessary for us, take warning from such; and it is true what I say, we know of worse deeds among the English than we have heard of anywhere among the Britons; and therefore there is a great need for us to take thought for ourselves, and to intercede eagerly with God himself. And let us do as is necessary for us, turn towards the right and to some extent abandon wrong-doing, and eagerly atone for what we previously transgressed;

Outside of moral narratives, however, English writers were keen to avoid any claims of kinship with the Danes; if comparison was drawn it was with the "Old Saxons", Christians, and leaders of the Holy Roman Empire. Sources like the Anglo-Saxon Chronicle refer to the Danes as "The Army" or "The Enemy" or, latterly "The Danes", against whom are usually arrayed "The Christians" or "The English" or sometimes "The People". Asser's Vita Ælfredi is more hagiographic: the Danes are always "The Heathens", in contrast to Alfred's Christian saviour figure.