It depends on a) how many people know about it b) how much they have to lose if the information gets out. The latter is a particularly powerful deterrent if it will hurt the person who shares it even if the leak isn't traced to them.
For the tank manuals a) is likely hundreds of thousands of people, and b) is zero unless the leak is traced to them, and they possibly don't expect much even if it is.
For the lab leak, b) is a strong deterrent - every virologist working on even moderately risky research would face trouble (in the form or stricter restrictions and possibly bans on the category of research) if the theory got confirmed, and for the people working in the Chinese lab, embarrassing the Chinese govt is probably pretty far up on the "mistakes you don't get to make twice" list. a) is less clear: They might not even be aware of a lab leak if it was one. However, one piece of sensitive info that could leak would be "we worked on something that was more similar to SARS-CoV-2 than the previously known sample", and I'd expect that to be reasonably well known at a research institute.
However, that adds a third aspect: Verifiability of the leak. Even if a drunk scientist sat in a pub in Wuhan, telling his friends that it totally was a lab leak, and someone overheard that - what then? They post on Twitter "I heard some people talking that it totally was a lab leak"? Even if their friends say "hey, I know someone from the place and it totally is a lab leak", it'd at best be yet another unconfirmed and unconfirmable rumor that would be unlikely to make it far.
Just because there are many leaks, doesn't mean there isn't also a lot of spicy information that never becomes public. These leaks are news because they're rare, even when hundreds of thousands of people have access to a piece of info. Reduce the circle of people in the know to 100, and the probability of a leak drops drastically.