[Bugs] When using a model from a BYOK provider, project skills fail to load

**Mood:** 😔
**Category:** Bugs

When using a model from a BYOK provider, it seems project skills are detected but fail to load when actualy trying to use thme or invoke them with a slash command.

The reason is silently failing.

This works fine when using models from the GitHub Copilot subscription.

---
| Field | Value |
| --- | --- |
| App version | 1.0.7 |
| OS | macOS 26.5.1 |
| Theme | IC Orange PPL |
| Path | /chat |
| Tenure | Day 3 (Week 1) |

首先使用 BYOK 提供商的模型复现该失败，然后将 project-skill 的加载和 slash-command 的调用与 GitHub Copilot 订阅模型进行比较。调查 BYOK 路径为何会静默失败；完成标准是两种情况下都能加载并调用 project-skill，并且在加载失败时提供可采取行动的错误信息。

由索引模型根据 Issue 内容生成。