The majority of Taiwanese people do not even consider themselves partially Chinese and none of the major political parties have any interest in political unification with China.
Some people in Taiwan might wish the people of China well because they have family there, but this is no different to how members of the Chinese diaspora around the rest of the world feel about the country.
The pro-China political parties in Taiwan are primarily right-wing parties, which is to say they are much more interested in the Chinese market than in Chinese politics.
There's an issue in how these polls are being conducted and it's hard to tell what's happening especially with Western articles that don't fully give all information or give the polling questions. The word "Chinese" have many different ways of stating it in Chinese. So when they ask in polls e.g. are you "Chinese", it really depends on which word they use. They can use 中国人, which does mean Chinese, but it also has a much stronger political connotation related to the mainland. So most people in Taiwan will say no they aren't 中国人, since they have their own government. However if you were ask, e.g. are you 华人 also a word for "Chinese", etc, they will more likely say yes. After all the official country's name is 中華民國. Mainland Chinese people will also say they are 华人 too.
For other readers, please note that 华 is the simplied form of 華. Outside of mainland China in Southeast Asia, most ethnic Chinese will refer to themselves as 華人/华人 -- roughly "Chinese descent". Most Chinese language speakers (and readers) in the region understand 中国人 to mean citizen of mainland China (and much more rarely Taiwan).
Making the 華人 distinction is like asking white Americans if they consider themselves ethnically European or Irish or Italian or whatever. Just as people in the US with European heritage may have an interest in what is happening in the nation of their ancestors, people in Taiwan with Chinese heritage may have an interest in theirs. But in neither of these cases do the majority of people see the nation of their ancestors as the country that they call home.
The context of these surveys in Taiwan is trying to determine if Taiwanese people see their own country as a different or perhaps more legitimate version of China, and the contemporary answer - unequivocally - is no. The only people pushing the myth that most Taiwanese people see themselves as citizens of China is the ruling party of China.
I don't think 华 is necessarily the same as ethnicity as it's interchangeable with the concept of "China" itself. 中華民國 translates into Republic of China the official country's name, of which Taiwan is mere province of. It's the same "hua". I think most Chinese historians recognize that China as a concept has often been "split" in the past, with different governments each stating their legitimacy. It happened e.g. during the Three Kingdoms period, the North and Southern dynasties period. It happened during the Song dynasty, etc., etc. It's happened an awful lot for long periods of time. To Westerners the Taiwan and China situation seems a bit odd, but not really in the context of Chinese history and the Chinese mindset. Regardless each government still saw themselves as the "legit" Chinese government with all that entails, e.g. mandate of heaven, etc..
If we are talking about ethnicity I believe that the large majority would say they are 漢人, which is more equivalent of an America saying he's Irish, Italian, etc. Huaren is more equivalent to saying you're Chinese, culturally, ethnically, etc... 华裔 is basically saying you have Chinese blood, which may be also different conceptionally.
中国人 used to not have such a huge political connotation to mean only PRC people but was more interchangeable with 中华, 华人, etc., but that's now not the case, and the polls reflect that change in mindset.
I don't disagree that there are many different overlapping terms and identities related to the concept of "China" and the people who have an ancestral connection to it. However, I think it is incorrect to blend all of these together and come out with the conclusion that at the end of the day there is only One China and One Chinese People and these concepts are immutable, inescapable and eternal.
The CCP and other historical leaders have used these concepts to try lay claim to every land that a Chinese person ever walked across, every sea they ever sailed and every fen they ever earned, but that has to be understood as the imperialism it is. Inside the empire it behooves the subjects to not publicly challenge that narrative, but outside of it people have the freedom to define themselves as they see fit.
Polling shows that the vast majority of Taiwanese people today do not consider themselves Chinese citizens (中國人), nor do they support Chinese unification (中國統一). If you put a Taiwanese person on the spot and ask them "well, in the context of the last five thousand years, could there ever be a scenario in which the island of Formosa is ruled by the same leaders as the region of East Asia along the Yangtze, Yellow and Pearl rivers?" they might say yes, because in those last five thousand years there were a couple of hundred when that was indeed the case. But that doesn't mean that they see themselves right now as having any deeper connection to the PRC than the Chinese diaspora in Singapore, Malaysia, Thailand, US, Canada or anywhere else.
I'm pretty sure at this point we are just talking pass each other. Taiwanese people don't consider themselves 中国人, because zhongguoren is now considered to mean a PRC citizen (although historically this was not necessarily the meaning). This is of course true, because Taiwan has their own government that runs pretty much independently from the mainland government. However, I don't think this means they don't see themselves as "Chinese", but simply that POLITICALLY they see themselves as not citizens of the PRC, but not necessarily that they aren't "Chinese".
And I think you're quite wrong that people in Taiwan don't have a deeper connection to Chinese in China. Diaspora in Singapore, Malaysia, Thailand, etc., have largely mixed with the indigenous cultures in those areas. Most of the later generations often speak a broken form of Chinese, or Singlish, etc., and if they do speak Chinese, perhaps they speak a Chinese dialect (brokenly) and probably practically illiterate in Chinese. In Taiwan this is simply not the case, by and large they all speak Mandarin and by and large all share the same history, know the same legends, pray to basically the same deities, can watch and read each others films/media, still uses the same flag as the one that represented China 80-100 years ago, often have close enough relatives still in China that aren't e.g. 5th removed since Taiwan's population double in size post '49, etc. Although there's a difference in traditional and simplified characters, it's not enough that someone who is fluent in one or the other and spends maybe a few months trying to learn the other would have much difficulty. Not to mention I believe most people say that if they already know traditional characters, it's easier to learn simplified, with simplified characters often being the running or grass script form of the traditional character. Moreover because there's actual communication between mainland China and Taiwan, Chinese spoken in both areas won't drift like it did between N.K. and S.K.
The same way you can be pro-Korea and anti-communist or, in the past, pro-Germany and anti-communist...
'China' does not mean the People's Republic of China, which is the communist state that occupies mainland China (from KMT's point of view). Taiwan is China, too.
Some people in Taiwan might wish the people of China well because they have family there, but this is no different to how members of the Chinese diaspora around the rest of the world feel about the country.
The pro-China political parties in Taiwan are primarily right-wing parties, which is to say they are much more interested in the Chinese market than in Chinese politics.