…22 Custom Endpoint support (#26126)

Updates the VS Code AI Gateway client docs to reflect the Custom
Endpoint provider introduced in VS Code 1.121 (Insiders) and promoted to
Stable in 1.122.

## Changes

**`docs/ai-coder/ai-gateway/clients/vscode.md`**
- Replace the deprecated `customoai` vendor with `customendpoint`
- Add the required `apiType` field (`responses` for OpenAI, `messages`
for Anthropic)
- Add Anthropic provider setup (Messages API type, base URL
`…/aibridge/anthropic`)
- Note GitHub sign-in is no longer required — works in
air-gapped/restricted environments
- Add limitation callout: inline suggestions and NES still require
GitHub Copilot
- Reflect the UI-first API key entry flow (VS Code stores the token
securely; do not paste into JSON directly)
- Drop the Centralized/BYOK split — VS Code has no template injection
path, so both scenarios follow the same user-driven UI flow

**`docs/ai-coder/ai-gateway/clients/index.md`**
- VS Code compatibility row: Anthropic `❌ → ✅`
- Updated Notes column

<details>
<summary>Research notes</summary>

- VS Code 1.121 shipped the Custom Endpoint provider (Insiders),
replacing the legacy OpenAI Compatible (`customoai`) provider which is
now deprecated.
- VS Code 1.122 promoted Custom Endpoint to Stable and removed the
GitHub sign-in requirement for BYOK.
- Anthropic support confirmed working: `apiType: "messages"` + base URL
`…/api/v2/aibridge/anthropic` (Coder's gateway accepts the Coder session
token as `x-api-key`).
- OpenAI uses `apiType: "responses"` + base URL
`…/api/v2/aibridge/openai`.
- API keys must be entered via the Manage Language Models UI — VS Code
stores them securely and references them as
`${input:chat.lm.secret.XXXXX}` in the JSON.
</details>

> This PR was drafted by Coder Agents on behalf of @matifali.

(cherry picked from commit 2211f9c)