Chat Editor: custom agent resets to Agent on first send

## Type: Bug

Regular VS Code Chat Editor using the Copilot Agent Host harness.

Discussion and screenshots: https://vscodeteam.slack.com/archives/C0AJZ5319PZ/p1788381749454329

## Reproduction

1. Open the VS Code repository in an Insiders editor window.
2. Open a fresh Chat Editor using the **Copilot** harness.
3. Select the real **Data** custom agent.
4. Send `hi`.

This reproduces again for every fresh session. After the first turn has completed, selecting Data again sticks for subsequent turns.

## Actual

The first request runs, but the newly established Chat Editor resets its mode picker from `Data` to default `Agent`.

## Expected

The real session created by the first send keeps the mode selected in the untitled Chat Editor, so `Data` remains selected while the request runs and after it completes.

## Root cause

`ChatService._materializeUntitledSession` creates and loads the real contributed-session model before sending the first request. It carries the untitled model's intended language model, but not the submitted chat mode. The request itself receives the correct custom `modeInfo`, while the real model bound into the widget still has its default `Agent` input mode.

The submitted mode must be transferred to the real model by whichever first send wins pending-request arbitration, including concurrent and late sends still addressed to the untitled URI.