"What the government probably doesn't like is the other way around, when normal people buy BTC with yuan and then sell them abroad, exporting capitals."
Don't they also get some type of currency back when they do this? which is probably then spent inside China too? I don't see how this would be different from the first scenario. Maybe I'm missing something.
It depends: if their goal is to export capitals, when they get foreign currency by selling the BTC they bought in China, they will keep that currency abroad and invest it there. Of course you can do the same with mining - instead of buying BTC at exchanges - but this will require first investing in China to buy China built mining equipment and operate your mine. That's the difference I see.
Don't they also get some type of currency back when they do this? which is probably then spent inside China too? I don't see how this would be different from the first scenario. Maybe I'm missing something.