What's the state of Chinese classical texts in the mainland after Simplified Chinese (and the Cultural Revolution)? In the past I've came across a few websites that distribute Buddhist texts in simplified Chinese, which is somewhat unsurprising since there's active interest in Buddhism to propagate once again in China. I'm not aware of a full canon in simplified Chinese, but I know there are many texts already converted so simplified.

But what about other formative texts in Chinese culture, such as Daoist and Confucianist? Or even Buddhist canons, since I'm not aware of one that was completely converted to simplified Chinese.

What kind of projects are there to preserve these texts in the modern script? Published books, websites..? Either by the government or private companies.

Are classic texts still teached in schools the same way they were before the introduction of today's simplified characters and the cultural revolution? Do they use traditional characters at all? How does one go about studying the classics nowadays?

Thanks!
I would like to answer your questions one by one at first, but I decide to give you a comprehensive answer here. I'll take Buddhism for example. Daoism and Confucianism (NOT a religion) are similar.
Buddhism are still publishing books in Traditional Chinese (TC). In fact, you can find both Traditional Chinese and Simplified Chinese (SC) versions of books existing in China. It is a widespread opinion that reading books in TC will be more beneficial than Simplified Chinese (SC), since TC is the script used back to the foundation of the two religions. Similarly, if someone believes Tibetan Buddhism, many lamas will require him to chant in Tibetan language. Such phenomenon is still common.
However, most experienced and renowned religious leaders (such as Master Jingkong and Dzongsar Rinpoche) are against such unnecessary restriction. Their opinions are: Since most Chinese now are taught SC, and religions should benefit as many people as possible, it's best to publish books and scriptures in SC, the most popular script in China. It should also be allowed to chant in Chinese language instead of Tibetan or Sanskrit, as it will make no difference except that Chinese people will find chanting much easier.
Traditional Chinese script is not taught in today's schools and universities in China, except for Chinese language major. However, it's not a big problem for the majority of Chinese to read TC due to the influence of Taiwan and Hong Kong(but most of them can't write it). For classical Chinese texts, they are still taught from primary school through high school, but they are all written in SC.
For Buddhism classics in Simplified Chinese, please visit:
http://www.fodian.net/index1.htm
This website cooperates with CBETA in Taiwan, which publishes corrected version of Buddhism classics.
You can leave a comment below if you have any remaining questions. Don't forget to give me an upvote or accept this answer if you find it useful.