Using `screenshot_page` tool without GitHub authentication provider stops chat

Without the Gihub Authentication Probvider, when Copliot creates a screenshot using the `screenshot_page` tool, the resulting screenshot is first displayed correctly in the chat, but afterwards the error message
```
Timed out waiting for authentication provider 'github' to register. (at tsx element zF > UU > fGe > Pxt > dl > > > m1t > Rxt > Mxt > r0)
```

is displayed, as well as in the Github Copilot Chat Output:
```
2026-08-14 16:29:58.874 [error] Error: Timed out waiting for authentication provider 'github' to register.
at gct.tryActivateProvider (vscode-file://vscode-app/usr/share/code/resources/app/out/vs/workbench/workbench.desktop.main.js:1222:80419)
at async gct.getSessions (vscode-file://vscode-app/usr/share/code/resources/app/out/vs/workbench/workbench.desktop.main.js:1222:76397)
at async gct.getAccounts (vscode-file://vscode-app/usr/share/code/resources/app/out/vs/workbench/workbench.desktop.main.js:1222:76121)
at async Xqt.$getAccounts (vscode-file://vscode-app/usr/share/code/resources/app/out/vs/workbench/workbench.desktop.main.js:1222:95830)
2026-08-14 16:29:58.896 [warning] [LanguageModelAccess] LanguageModel/Embeddings are not available without a Copilot token source
```

- Copilot Chat Extension Version:
- VS Code Version: 1.133
- OS Version: Fedora 44
- Feature (e.g. agent/edit/ask mode): agent
- Selected model (e.g. GPT 4.1, Claude 3.7 Sonnet): Qwen3.6-35B-A3B-UDQ6KXL

Steps to Reproduce:

1. Start VSCode using code --disable-extension vscode.github-authentication, configure a BYOK model
2. Activate the "screenshot_page" tool and use the chat in agent mode with
```
Navigate to
http://localhost:8080/

and make a screenshot of the page.
```

Workaround:
Patch the methods `$getSession` and `$getAccounts` to return null and [], i.e. :

`$getSession(e,t,i,n,r){` --> `$getSession(e,t,i,n,r){return null;`
and
`$getAccounts(e){` --> `$getAccounts(e){return [];`