The thing is LLM generate token by token and if you have to write entire css before writing the html, the quality could be worse.

You could prompt the LLM to define styling using inline `style` attributes; and then, once you've got a page that looks good, prompt it to go back and factor those out into a stylesheet with semantic styles, trading the style attributes for sets of class attributes.

Or you could tell the LLM that while prototyping, it should define the CSS "just in time" before/after each part of the HTML, by generating inline <script>s that embed CSS stanzas as string literals, and which immediately inject those into the document using CSSStyleSheet.insertRule(). (This can, again, be cleaned up afterward.)

Or, you can keep your CSS and your HTML separate, but also keep an internal documentation file (a "style guide") that describes how and when to use the CSS classes defined in the stylesheet. This is your in-context equivalent to the knowledge the LLM already has burned-in from training on the Tailwind docs site. Then, in your coding agent's instructions, you can tell it that when writing HTML, it should refer to the "style guide", rather than trying to reverse-engineer the usage of the styles from their implementation in CSS.