I updated VS Code to the latest version and now, when I press F5 to debug, it says 'Extension host terminated unexpectedly'.

And then, when I restart the extension host (whatever that is), the following error is printed:

Error: The Kha task detection didn't contribute a task for the following configuration:
{
    "type": "Kha",
    "target": "Debug HTML5",
    "problemMatcher": [
        "$haxe-absolute",
        "$haxe"
    ],
    "group": {
        "kind": "build",
        "isDefault": true
    }
}
The task will be ignored.

Is this a VS Code bug?

I don't know. I'm on the latest vscode myself (1.38.1) and can not reproduce that problem.

Right, I did a clean install of VS Code and gitted the latest Kha, only now, when I hit F5, there is this warning:

kha/graphics4/PipelineState.hx:111: Warning: Sampler tex not found

and the assets are not copied to the target folder.

The warning is normal but no idea about your assets. That works with a normal node Kha/make call?

Yes, I believe so. This is the terminal output, when hitting F5:

> Executing task: node C:\Development\Kha\make.js debug-html5 --debug <

Using Kha from C:\Development\Kha
Creating Kha project.
Compiling shader 1 of 8 (painter-colored.frag.glsl).
Compiling shader 2 of 8 (painter-colored.vert.glsl).
Compiling shader 3 of 8 (painter-image.frag.glsl).  
Compiling shader 4 of 8 (painter-text.frag.glsl).   
Compiling shader 5 of 8 (painter-text.vert.glsl).   
Compiling shader 6 of 8 (painter-video.frag.glsl).  
Compiling shader 7 of 8 (painter-image.vert.glsl).
Compiling shader 8 of 8 (painter-video.vert.glsl).
Done.

Terminal will be reused by tasks, press any key to close it.

And this is the khafile.js:

let project = new Project('MyProject');

project.addAssets('assets/**');
project.addSources('sources');

resolve(project);

There are loads of files in the 'assets' folder, but none are copied to the 'build/debug-html5' folder.

When I revert back to Kha 19.2 (the extension downloaded from within VS Code), everything works fine in Debug-HTML5.

So when you execute it on the terminal the assets are copied over?

The assets are copied to target build folder only in Kha 19.2. When I'm using the latest Kha from github, no files are copied. I tried debug-html5 and android-native targets without success.

File a github issue with a sample khafile please.