In summary, the base druid and cleric classes offer a good selection of thematic spells, with each class having one subclass in particular that is more on-brand than the others.
Druid, with Circle of Stars being the most thematic subclass.
The Druid class offers several divinatory spells:
- locate animals or plants
- locate object
- find traps
- detect magic
- detect poison or disease
- locate creature
- commune with nature
- scrying
- find the path
Additionally, the expanded spell list from Tasha's Cauldron has a couple more:
This makes for a pretty complete selection of spells with the theming you are looking for. As for subclass, the most on-brand is probably going to be the Circle of Stars:
The Circle of Stars allows druids to draw on the power of starlight. These druids have tracked heavenly patterns since time immemorial, discovering secrets hidden amid the constellations. By revealing and understanding these secrets, the Circle of the Stars seeks to harness the powers of the cosmos.
Many druids of this circle keep records of the constellations and the stars’ effects on the world. Some groups document these observations at megalithic sites, which serve as enigmatic libraries of lore. These repositories might take the form of stone circles, pyramids, petroglyphs, and underground temples— any construction durable enough to protect the circle’s sacred knowledge even against a great cataclysm.
None of the class features do much in the way of divining information, but the 6th level feature functions similar to the Divination Wizard's Portent, giving a reaction that either helps or hurts an attack rolls, saving throw, or ability check based on dice rolled at the end of a long rest.
Cleric, with Knowledge Domain being the most thematic subclass.
Like the Druid class, the Cleric spell list has good options for your idea:
- locate object
- find traps
- detect magic
- detect poison or disease
- detect evil and good
- locate creature
- clairvoyance
- divination
- commune
- legend lore
- scrying
- find the path
The Knowledge domain further adds the spell augury, and offers some on-brand subclass features, with the 6th level feature offering a thought detection Channel Divinity option, and the 17th level feature, Visions of the Past, allowing you to divine recent events happening to an object or area.