Does VS Code publishe schema files for launch.json or any other of its json files? I've found tasks.json, but can't find any other json files.
The tasks schema is generated at runtime. Quoting Alex Ross (one of the VS Code maintainers):
Our schema isn't entirely static, we build it at runtime. Some things are easy to document (like dependsOn) but others, like tasks types, are added to the schema based on what extensions, included built in extensions are installed. So in addition to the types you list, you could have many more from installed extensions.
VS Code does provide a reference page for general properties of tasks.json, but apparently some of it is out of date.
Pretty much the same goes for launch.json. The schema is generally specific to each debug configuration type and documentation can be found in each of the corresponding language documentation pages under their documentation. Ex. nodejs, c++, python, though there are attributes that are mandatory, optional, and conventional.
A lot of actual json schema files can be found at schemastore.org, but I don't think that can be said for tasks.json and launch.json.
If your goal is to use the schemas, you can put "$schema": "vscode://schemas/tasks", or "$schema": "vscode://schemas/launch", in the JSON file, and VS Code will understand it. I suspect you could also use those URLs in the json.schemas setting, though I haven't tried.