Theme.json: creating different sections of the color palette

No, writing as of WordPress 6.0 there is no API for defining additional palette sections. The colour palette component hardcodes 3 PaletteEdit sub-components, theme, default, and custom, where custom is for user defined colours. No dynamic fields or slotfills are provided for extending or adjusting these. Here is the current code:

    return (
        <VStack
            className="edit-site-global-styles-color-palette-panel"
            spacing={ 10 }
        >
            { !! themeColors && !! themeColors.length && (
                <PaletteEdit
                    canReset={ themeColors !== baseThemeColors }
                    canOnlyChangeValues
                    colors={ themeColors }
                    onChange={ setThemeColors }
                    paletteLabel={ __( 'Theme' ) }
                />
            ) }
            { !! defaultColors &&
                !! defaultColors.length &&
                !! defaultPaletteEnabled && (
                    <PaletteEdit
                        canReset={ defaultColors !== baseDefaultColors }
                        canOnlyChangeValues
                        colors={ defaultColors }
                        onChange={ setDefaultColors }
                        paletteLabel={ __( 'Default' ) }
                    />
                ) }
            <PaletteEdit
                colors={ customColors }
                onChange={ setCustomColors }
                paletteLabel={ __( 'Custom' ) }
                emptyMessage={ __(
                    'Custom colors are empty! Add some colors to create your own color palette.'
                ) }
                slugPrefix="custom-"
            />
        </VStack>
    );

https://github.com/WordPress/gutenberg/blob/a5ef504432e34afc0792eae62e44d71590c031eb/packages/edit-site/src/components/global-styles/color-palette-panel.js

Changing this will require a new API to be added to the block editor. I’d suggest creating an issue on the gutenberg github repo for this if one doesn’t already exist.