The association of JSON schemas to files is done in the settings (File, Preferences, User Settings or Workspace Settings), under the property 'json.schemas'.

This is an example how the JSON schema for bower is associated to the bower schema.

"json.schemas": [
    {
        "fileMatch": [
            "/bower.json",
            "/.bower.json"
        ],
        "url": "http://json.schemastore.org/bower"
    },
    ...

You can also use schemas located in your workspace or define a schema right in the settings itself. Check https://code.visualstudio.com/docs/languages/json for examples.

Figured it out: url was missing a leading dot, like this:

"jsonValidation": [{
    "fileMatch": "*.testing",
    "url": "./schemas/testing.schema.json"
}]

When url starts with this ./ pattern, it is automatically understood to be a file that shipped with the extension. If the ./ or even just the . is missing off the front, it will be treated as a URL to be fetched from a server instead.

Since vscode is open source, I can reference the line of code that implements this behavior.

It's here: jsonMain.ts#L105

If you want to use a relative path to something in a workspace folder for the url property of a JSON schema setting item, you need to define that setting in the workspace settings (<workspace-folder-path>/.vscode/settings.json) instead of in the user settings. Related docs are here.

If you insist to define it in the user settings.json, I think you need to use an absolute path.

I think this is a sensible design. User settings apply to all workspaces, so if if relative paths were supported there, it would be an assumption that every single folder you open as a workspace would have a schema file that you'd want to use at such a path (presumably relative to the workspace folder, which I think would be a rather poor assumption, or lead to surprising users (in a bad way)).

Also note that if you want to specify schema files on a per-JSON-file-basis, you can use the $schema property in the JSON file you want to be validated to specify the schema to use.

If you have a scheme like file:, that forms a full (absolute) URI, instead of a (relative) URI Reference.

A full URI is supposed to mean the same thing everywhere, so it doesn't make sense to have a relative file path. Also note that file:///foo.schema.json is the same thing as file://localhost/foo.schema.json

To write a relative filename, use a URI Reference, like foo.schema.json. This will be resolved against a URI base — typically the URI of the document — to form the correct URI, even if the file moves on the filesystem.

For example, if you use this in a file at c:\test\main.json, then the Base URI will be file:///c:/test/main.json, and the URI Reference will resolve to file:///c:/test/foo.schema.json, which is correct.

See File Uri Scheme and Relative Files for more information on this.

I found out it's possible to provide those JSON Schemas. In settings.json there are a couple of examples for Bower and package.json

They are under "json.schemas".

Go into File > Preferences > Settings, search for JSON and find the following setting: JSON > Schema Download: Enable

If you toggle that off and on VS Code will grab the latest version of the schema files.