(This also applies to other lanterns)

The only reasonable explanation is that the ring can change size depending on who is wearing it. I don't really have any evidence though.

Yes, as the Ring of power resized from Sauron to Isildur and then to Gollum, Bilbo and Frodo.

I remember seeing the Green Lantern rings adapt to the wearer in animated versions of the stories

Right, that always seemed to be the assumption. They’re physical manifestations of the strength of willpower. They’re not simply objects forged from metal. It only makes sense that they can shift size to fit the need of their owner.

The ring modifies itself to the benefit of the wearer, this has been shown multiple times like when Dex-Starr got his Red ring, the ring changed size to fit his tail. The Green Lantern ring does the same thing, the rings themselves have something akin to a conscience, they have been shown moving it's wearer while the Lantern is unconscious and keeping them alive in space.

I could have sworn it has been mentioned but the more I think about it it’s probably always be assumed.

Based on the assumption, because the rings have a form of sentience they can adjust themselves accordingly to the wearer they select; however, as they are still tangible materials they can only change to the limit of their mass. If they could assume any size then Mogo’s ring would encircle his equator, not hide in his core. Bzzd would have a tiny one around his limb, not around his waste. Likewise, Dex-Starr’s would be on his paw, not his tail. The only ring that doesn’t fit this format, and fittingly so, is G’nort.

It could also be that a Lantern has some choice in the matter... For the examples of Mogo and Dextarr, it could simply be more convenient for them in those positions rather than in a conventional spot.

This was Mogo's ring back in the day