The leaked Pokedex entries are as follows:
Enamorus (Incarnate)
“When it flies to this land from across the sea, the bitter winter comes to an end. According to legend, this Pokémon’s love gives rise to the budding of fresh life across Hisui.”
Enamorus (Therian)
“A different guise from its feminine humanoid form. From the clouds, it descends upon those who treat any form of life with disrespect and metes out wrathful, ruthless punishment.”
As far as weather goes, it brings an end to brutal winters. It seems to bring fertility among creatures, which mirrors Landorus bringing fertility among crops. One can assume, based on these entries and the heart shape on its head, that it represents love. As for its inspirations, it is based on the Xuanwu from Chinese mythology-a tortoise depicted alongside a snake, just like the Therian form. The Xuanwu is part of the Four Symbols of the Chinese Constellations, and the other 3 are the inspirations for the other 3 “genies.”
Source for the Pokedex entries