Serve /api/config endpoint with managed connections

## Parent PRD

#1660

## What to build

Add a `GET /api/config` endpoint that returns the client-relevant subset of the config file (everything except the `server` block). This replaces the current `/defaultConnection` endpoint and `defaultConnection.json` file generation.

The endpoint returns connections (keyed by stable ID with name, url, queryEngine, authentication, fetchTimeout, nodeExpansionLimit), feedbackUrl, and any other client-relevant fields. The `server` block is filtered out since it contains server-only settings.

## Acceptance criteria

- [ ] `GET /api/config` returns client-relevant config as JSON
- [ ] `server` block is excluded from the response
- [ ] Connections include their stable key/ID in the response
- [ ] Returns empty connections object when no config file is present
- [ ] Old `/defaultConnection` endpoint removed
- [ ] Integration tests for the endpoint with various config states

## Blocked by

- Blocked by #1661

## User stories addressed

- User story 1
- User story 7

## Related Issues

- Part of #1660

首先跟踪现有的 /defaultConnection 端点和 defaultConnection.json 的生成过程，然后检查配置文件和受管理连接的表示方式。当 GET /api/config 返回包含稳定连接 ID 的客户端相关 JSON、排除 server、在缺少配置时使用空连接、移除旧端点，并且针对所述配置状态具有集成测试覆盖时，工作即完成。

由索引模型根据 Issue 内容生成。