You can design the two buttons, then use conditional visibility to show one and hide the other. Conditional visibility will target your categories.
You can also define the image as a field of your categories. So an image field in your category collection, named “icon of the button”. And you can also define a bg color as a color field if you want.
Now in the Designer, you’ll select the vutton, go to settings tab and click on use bg color and use bg image from a colection, and target the category icon and bg color.
Solution 2 is better. It allows you to change the color and the icons when you want and have to changes pushed to the entire site.
If you have trouble to put that in action, add the icon and color fields to your category collection then generate a sharing link and paste it here.
You want to emohji to be native emoji, like text emoji? It’s a bit risky as they don’t render the same on various systems.
But anyway, you can have an imge in the collection, and use it as a background image on your dynamic element. It’s possible with webflow (select element, go settings tab and check “use image as background” in the purple otpions. Same can be done with color.) Then you can place the image finely using bg controls in the style panel (add a bg image and don’t specify it, if it’s not automatically created) and padding.