Web VS Code extensions cannot activate `ms-vscode.wasm-wasi-core`

When writing a web-only VS Code extension, i.e. with a package.json that only defines a "browser" entrypoint, the extension will not activate when depending on ms-vscode.wasm-wasi-core:

"extensionDependencies": [
    "ms-vscode.wasm-wasi-core"
]

Minimal working example:

• Install the WASI based WebAssembly Execution Engine from the Marketplace.
• Download the official lsp-web-extension-sample example.
• Add ms-vscode.wasm-wasi-core as an extension dependency and run.
• The extension will not activate and will display the error:

  Cannot activate the 'lsp-web-extension-sample' extension because it depends on the 'WASI based WebAssembly Execution Engine' extension, which is not loaded. Would you like to reload the window to load the extension?
  

  Reloading the window does not fix the issue.

Tested on Mac (with the default "Run Web Extension" launch option; VS Code 1.94.0, on Sonoma 14.6.1), and also within a self-hosted web environment.

Reproduce the failure with the lsp-web-extension-sample, its package.json browser entrypoint, and the default "Run Web Extension" launch option. Trace why the ms-vscode.wasm-wasi-core dependency is reported as not loaded in a web-only extension, then verify that the sample activates successfully without the reload error in the tested web environments.