**The herb and pepper oils are very unlikely to explain it. Cooling and fat crystallization are the more plausible causes**, although the cooling time and actual temperature would be needed to pin it down.

Your intuition about the quantities is sound: a handful of herbs contributes very little oil compared with 12 ounces of butterfat. For scale, a [2019 basil study](https://www.mdpi.com/2073-4395/9/6/279) measured just 0.02–0.17 grams of essential oil per 100 grams of fresh basil.

Butterfat sets by forming a network of fat crystals. Melting destroys that network, and rebuilding it takes time; its texture depends on both temperature and cooling history. A batch can therefore remain fluid at a temperature where previously set butter holds its shape. Clarified butter can also have solid grains suspended in liquid fat. [Tetra Pak’s dairy handbook](https://dairyprocessinghandbook.tetrapak.com/chapter/butter) explains how crystallization governs butter’s consistency.

**Refrigerate a small portion for several hours or overnight.** The fat should become firm. If it does, that strongly supports a cooling/crystallization explanation. If a separate watery layer remains, the fresh ingredients may have introduced moisture that stayed behind.

Incomplete straining would explain flecks or cloudiness; ordinary amounts of leftover herb or milk solids would not keep the entire butterfat portion liquid.

For storage, treat this as a fresh herb infusion: refrigerate promptly and use within four days, or freeze. That follows [university extension guidance for homemade herb-infused oils](https://class.ucanr.edu/sites/default/files/2020-12/341230.pdf).