Historically Greenland was part of the Diocese of Nidaros, may this have been to distant? Would Greenland having a more native church infrastructure be more connected to Europe?
No. Never a part of diocese.
Part of province. And that was very relevant.
OTL Greenland was part of Diocese of Skalholt from 1056 to 1126, thereafter Diocese of Gardar.
And part of Province of Bremen till 1104, then Province of Lund till 1152, then Province of Nidaros.
Now imagine a significant Christian Vinland settlement.
OTL, Iceland had 2 dioceses (Holar was split from Skalholt in 1106), Faroes had one for themselves since 1047, Orkney and Shetland one for two since 1035.
In 1126, Greenland was a sizable Christian settlement - but, like Faeroes, nowhere left to expand.
TTL, with Vinland an appreciable Christian settlement and a potential missionary field - I´d expect a Bishop of Vinland quite early. Say 1107 (1106 for Holar was no coincidence).
And a bigger political butterflies...
OTL, in 1151, Papacy made a political decision to give each Scandinavian kingdom their own Archbishop.
Norway got Nidaros in 1152. In Sweden, civil wars delayed founding of Province of Uppsala till 1164, but the decision had been made.
Now, Norwegian kingdom obviously got the dioceses they ruled. Norway, Orkney, Faroes, Sodor and Man.
But the commonwealths of Iceland and Greenland were just 3 dioceses between them - poor and no prospects. Which is why they were subordinated to Nidaros.
In TTL, where Diocese of Vinland is an expanding settlement and missionary area?
An obvious reason to make Vinland a metropolis, too.
And given the existence of Province of Vinland, who would Iceland prefer? Archbishop of Nidaros (controlled by King of Norway) or Archbishop of Vinland?