Ever since I heard about during the pandemic, it has been my dream to visit CLI, a language school in Guìlín (桂林) for two weeks of learning Chinese. Now that the PRC borders opened, it seems to have become possible. I contacted the school and heard that it's now possible to obtain X2 visas, from which I inferred that this might be the visa type I should pursuit. I find it difficult to find concrete information about this type of visa though. Given that I'm not a university student anymore, is it actually the right type? Would it offer me any advantages/have extra requirements compared to the regular tourist visa?
X (Xuexi) studying visas should be used whenever your main purpose in China is to attend an accredited institution, not necessarily a university.
While studying does not require a specific authorization under Chinese entry regulations (unlike working), your purpose of stay must still be consistent with your visa category. If you are enrolled in a full time program more than a couple days, it is likely that your main purpose is considered study instead of tourism.
In any case, if they are registered with the local education department, (which they are legally required to be), their acceptation certificate can be used for X visas.
FWIW, the Chinese version of the school website looks like a machine translation (a very good one, but still many strange expressions that evoke English syntax). This may be just laziness if the website was developed by non-Chinese native speakers, but nonetheless it is good to ask about their accreditation from the local education bureau 教育局.
Contrary to some countries, a Chinese tourist visa very likely doesn't allow you to study under it
The FAQ for the visa center reads
What is the major purpose of your visit to China and which is the most appropriate visa category for your application
|Major Purpose of Visit
|Description of Visa
|As a tourist
|Issued to those who are going to travel to China for tourism.
|As a student
|Issued to those intending to study in China for a period of no more than 180 days
You are not going there for tourism, and you are studying Chinese
Since the information about what's allowed or not under a visa, is really sparse, as far as I can found, I'd suggest you follow the advice of the school and get a X2 visa