First, terms like "Sinosphere" have variable usages and definitions, and it's not really productive to ask the question as worded in your title. There's no question that Zhuang is much more heavily influenced by Sinitic than other Tai languages not spoken in what is now China. You can't find a lot in talking about the Sinosphere because it's not a meaningful category. We can talk about things like Sino-xenic readings (Sinitic loans in Korean or Vietnamese, for example) as useful, but this isn't how we would or should go about approaching a language as a whole.

So like, you ask:

How do the Zhuang people fit into the overall Sinosphere? What makes them similar to the other Sinosphere cultures and what makes them distinct?

How are you defining Sinosphere? Zhuang is a Tai language, not a Sinitic one, so it can't be on linguistic grounds. If you mean Sinosphere as only "stuff in China", that's also not a historically useful way to delineate topics, since the borders are constantly changing and people migrating. If you mean it more generally as "the world under the influence of what we today call China (even though things were much more complicated than that)" then I think sure, Zhuang is reasonable to include, but only if we're recognising the lack of premeation of Chinese culture into the areas where Zhuang and languages like Jinghpaw were/are spoken. Which is to say, only in modern times do I think this is appropriate to be included, because really only in modern times, especially since the 1950s, as a large-scale effort been made to bring them in.

Adding to that thread,

And is there enough similarities that we should start seriously including the Zhuang culture into our studies of the Sinosphere on equal footing with Japan, Korea, Vietnam, and China?

Part of the reason we consider Japan and Korea under the Chinese sphere of influence is because of a clear effort by those places to adopt large chunks of Chinese culture wholesale. We can simplify this idea by saying that it's not that there was Chinese culture and Korean culture in the view of people back then, but rather that there was just Culture, and China had a monopoly on it. However one place that was more or less free of these influences (with a few obvious exceptions) was Siam; the Tai-speaking world had its own internal order, system of law and governance, trade and all the rest. You could almost draw a line north of where the Mueang system of city/citystate organisation was prevalent and call that the end of China's greatest influence. That's a bit of a simplification, and there are plenty of cases that fall in-between, places like Nanzhao that by most accounts had their own thing going for them which were neither Sinified nor within what we could call the SE Asian Pali-sphere (modern Myanmar, Thailand, Laos etc. Places where Pali-language influence was considerable and a common form of Buddhism predominated daily life).

Second, Zhuang is not one language. It's a dialect continuum, or rather a couple continua, and there are considerable differences between Northern Zhuang and Southern Zhuang. That they are both called Zhuang is more a result of the PRC's ham-fisted classification of minority languages than any actual relatedness of speech varieties or separation from other Northern Tai varieties. See literally almost any other of the 55 official ethnic minorities for another likely example of bureaucracy ignoring linguistic and cultural reality for the people being classified.

Then finally, there is actually a massive amount of information out there on Zhuang. A lot of it is found in journals that otherwise work on Tai-Kadai, and the majority of it is written in Mandarin or Thai rather than English, but there's still plenty in English. Unfortunately I'm at home right now (it's Sunday) and the books I have on Zhuang are in my office, which I'd rather not trek to on a Sunday afternoon just for this. But it's all out there, and any conference on Tai studies has the potential to have at least one presenter talking about Zhuang. The Journal of South East Asian Linguistics is relatively small, but that might be a place to look. However, they're going to be papers that are not written for a general audience, and so might not be what you're looking for.

But rest assured it's out there and there are a lot of people working on Zhuang both within linguistics and anthropology.

If you have other questions I'm happy to answer. But for the general "is this a thing" question the answer is yes.

edit because I forgot to mention Sawndip: Be careful with how you think about things like writing systems. In many cases, including Sawndip and Chữ Nôm or Gugyeol, it was a lot less cohesive and standardised than you may think. On that point actually the same can be said for Chinese Chinese characters. While certain frequent characters were more uniformly used in such systems, a huge amount of variety existed, both regional and even for a single community. Compare this to English before our still-not-really-standardised spelling became as standard as it is. Read some old letters from the 1700s and you'll see all kinds of variation. The same thing can be seen with ideographic systems, including Chinese, and including Chinese even recently. So don't take the elevation of Sawndip in modern discussions of Zhuang as indicative that it was a uniform widely-used system that guarantees membership in the larger group we're calling the Sinosphere here. Also also, don't forget about things like Tangut, and you'll start to see why copying the Chinese writing system becomes a less useful diagnostic tool. Writing hasn't actually been invented that many times in human history, and most systems are adaptations of someone else's systems, so again as a western analogy, it would be like lumping Greek, Russian and English together.