That’s entirely up to you. Search engines automatically rank the most relevant content possible for search queries that serve at least some quality. Categories are often of “low quality”: They don’t describe a full, coherent story people tend to peruse.
For these reasons, it’s why you won’t see many categories appear in Google Search. Oversimplified, they rank content based on the number of clicks they receive, and the number of bounces (navigate back to search engine) they get thereafter. Categories suffer from those bounces.
Still, categories can be helpful to have indexed for the reasons I left in my first reply: it allows search engines to crawl them, find new content, and mark your posts as relevant thanks to the internal links they supply. If you create a second category later, consider how helpful it is for visitors that land on there via search engines, but also how valuable it is for internal linking.
You can learn more about how search algorithms work here (Relevance & Quality of content): https://www.google.com/search/howsearchworks/algorithms/.
Having superfluous content indexed isn’t necessarily a bad thing (exceptions apply). It just slows down the crawling rate of the search engine on your site. But, if you don’t need new content indexed frequently and immediately, or have fewer than a couple of hundred pages, then it’s OK to have a bit of content indexed that’s questionable in usefulness.
The exception is when you have more useless content than useful content. That is why we apply “noindex” to Media, Date, and Search pages by default. And that’s also why our “Advanced Query Protection” is enabled by default for all new sites.
As for that “Apply noindex to categories” box: You’re free to check that–you can overwrite that on a per-category basis later.
I think this covers everything you need to know! Cheers ??