Currently, theme.json does not let you style the citation field for the Quote and Pullquote blocks.

It should be possible to (for example), set a font size for the main quote, and set a specific font size for the citation as well. Or to use different fonts for each. Here's some pseudocode for example:

"core/pullquote": {
	"typography": {
		"fontFamily": "var(--wp--preset--font-family--source-serif-pro)",
		"fontSize": "var(--wp--preset--font-size--huge)",
		"fontWeight": "300"
	},
	"citation": {
		"typography": {
			"fontFamily": "var(--wp--preset--font-family--system)",
			"fontSize": "var(--wp--preset--font-size--small)",
			"fontStyle": "italic"
		}
	}
}

Here's an example of what we'd like to achieve for the pullquote block in Twenty Twenty-Two, but cannot at the moment:

The main issue in that specific case is that I cannot use one font for the quote, and another font for the citation.