Take this with a grain of salt because I'm more of a brand, content, and SEO strategist + copywriter more than a product maker (though I'm learning!). I'd recommend not actually monetizing the tool, but monetizing the audience.

If you add friction to using your tool, people will just go elsewhere because there are tons of free palette generators so why wouldn't they. But if you already have something people trust, you could add something like "get the full UI kit" button that leads people to a paid pack of Figma components, Framer templates, or CSS themes already styled with those exact colors. This requires knowing your audience and knowing what they use the palettes for, though.

I'm not sure how or if that's possible to automate this, but I'm thinking of ways you can take an existing audience and continue to remove friction for them by using your tools -- in this case, removing the necessity for them to apply the palette they've generated for free by themselves.