As discussed before, tags already do most of what you ask.
Create a tag group called “topic type”, add the tags you want, make it required.
See Tag icons component. That handles changing how tags look.
If you don’t like the way that tags are selected, you could get a theme component that would let you select them as in your image rather than the existing interface. I’m not sure how much work it would be but if you have a budget, you can commission a checkbox tag selector theme component.