So I believe that me and Trinity Seven wiki fandom interpret it correctly for the following reasons:
1. The fact that they put the archives and T7 mages in the normal world
in comparison with the clouds and the heavenly adjudicators in the heaven heavily implied that the relationship between the archives and T7 mages has no difference from the relationship between the clouds and the heavenly adjudicators at all (That is,
if the archives exist in a higher dimension than T7 mages, so do the clouds exist in higher dimension than the heavenly adjudicators).
4. So if my three points above are correct, then "something of higher dimension" can only mean "clouds of higher dimension", which in turn, means that they belong to the higher dimension as a part of it. So the 6-D clouds remain unchanged, the whole "clouds link to the gods" stuff will just simply mean that they link to the gods while still existing in their higher dimension rather than being contradicted by any chance (for example, you can have a 6-D being having immortality as long as 100-D still exist, they are connected but not leading to anti feat obviously).