Update inline code styling to light gray fill with no stroke

Summary

Added custom CSS styling for inline code tags (text wrapped in backticks like test) to display with a light gray background (var(--grayscale-3)) and no border. The styling targets only inline code within prose sections, excluding code blocks.

Review & Testing Checklist for Human

• Visual verification in light mode: Check that inline code (e.g., example) has a light gray background and no border on documentation pages
• Visual verification in dark mode: Verify the styling looks appropriate in dark mode (the --grayscale-3 variable should adapt)
• Code blocks unaffected: Confirm that multi-line code blocks still render correctly and are not affected by this change
• Readability: Ensure the light gray background provides sufficient contrast and doesn't make inline code harder to read

Test Plan

1. Generate a preview of the docs with fern generate --docs --preview
2. Navigate to pages with inline code examples (e.g., CLI reference, SDK documentation)
3. Toggle between light and dark modes
4. Verify inline code styling looks correct and code blocks are unaffected

Notes

• Requested by [email protected] (@jon-fern) via Slack
• Link to Devin run: https://app.devin.ai/sessions/096d9173bf654933b748a5dd47ca4cd6
• The CSS selector .prose code:not(pre code) specifically targets inline code while excluding code blocks
• Using the existing --grayscale-3 CSS variable for consistency with the design system