[Feature Request] Implement lazy-loading of connector tool schemas and Tool Access Mode settings

Bug Description
Connector tool schemas aren't lazy-loaded the way they are in claude.ai. A single haiku message outside of any project folder exceeds token limits in claude code but chat/cowork remain usable. Claude Code needs the same "Tool access mode" options that web/desktop chat & cowork have.

Environment Info

• Platform: darwin
• Terminal: Apple_Terminal
• Version: 2.1.274
• Feedback ID: 25e60cc8-4321-4136-9fc3-e4d18f3b2e10

Evidence

Claude Code CLI conversation attempt:

▎ Using Haiku 4.5 (from .claude/settings.json) · /model ❯ HI ⎿  Prompt is too long · the request is ~214744 tokens (limit 200000) but this conversation is only ~9923 tokens — the rest is system prompt, tool definitions, and attachment content. A single-exchange conversation cannot be compacted; reduce attached files/tools or start with less context. · /clear to start fresh

Claude Desktop Chat:
<img width="866" height="533" alt="Image" src="https://github.com/user-attachments/assets/795780fd-21f0-4f53-a0dc-87c46cbe63aa" />

Claude Desktop Cowork:
<img width="880" height="522" alt="Image" src="https://github.com/user-attachments/assets/d1ebe33e-2c77-445e-9ad9-bf6753525b13" />

Claude Desktop Code
<img width="871" height="529" alt="Image" src="https://github.com/user-attachments/assets/b54e1c5a-40e3-4856-8b3a-0518ec91a549" />