I keep a bookmarks folder of websites that have non-cookie-cutter design.

If I have an aesthetic in mind I'll use some screenshots of those sites in the prompt and phrase their inclusion as: "Look at these slightly non-standard designs that work really well for me." So far I've only seen Claude look for through-lines and high-level takeaways--"user likes <design feature> based on the screenshots, so I'll include that"--and screenshots aren't currently a granularity level where it can lift specific details or produce something derivative.

Other than that I try to encourage specific consideration of: type scale, borders and rounding, padding/whitespace, elevation as shadow vs blur, colors. I don't think one needs to pull every customization lever on every project.