Your question was, "What would be an idiomatic option?" as to how to finish the sentence
"The government censors 80 percent of websites. In this country the Internet censorship is quite ....?"
I suggest "severe" (Merriam-Webster) for a single-word answer:
strict in judgment, discipline, or government; rigorous in restraint, punishment, or requirement.
Otherwise, your construction (as currently edited with the order of statements reversed) is idiomatic and good English. I would prefer to combine the two sentences into one:
In this country Internet censorship is severe: the government blocks
access to 80 percent of websites.
This source, for instance, explains that
A colon instead of a semicolon may be used between independent clauses when the second sentence explains, illustrates, paraphrases, or expands on the first sentence.
However, stating it as two sentences is perfectly acceptable.
By the way, I love the word "draconian" (and up-voted the answer by @Centaurus as well), but depending on your audience it may not be as readily understandable (and therefore not as idiomatic) as a more common term like "severe."