The tools themselves are not secret, the private data contained in them is. So I would say you can post bug reports publicly about the mod tools, as long as you remove any private data that would be visible.
For the private messaging tool that would mean not using a real private message that contains user information. For the flag list or the moderator overview you would have to edit the screenshots and blank out any sensitive information. It might be easier in some cases to just use a private channel for reporting those, then.
I remember a few bug reports with screenshots of mod tools (e.g. this one or this one or this one from myself), and I haven't seen any complaints about these.
The exception are the tools for detecting sock puppets or vote fraud, I don't think those should be revealed. Bug reports for those I'd make directly in the Teachers Lounge or via mail to the team.