[Feature Request] Support fetching claude.ai shared conversation links in Claude Code

Bug Description
Title: [Bug/Feature Request] Claude Code cannot access claude.ai shared conversation links

Body:

Claude Code cannot fetch content from claude.ai/share/* URLs — the server returns 403. This blocks a natural workflow where a user researches a topic in Claude.ai, generates a shared link, and
wants their Claude Code session to incorporate that research.

The workflow that fails:

1. User has a detailed conversation in Claude.ai about deployment architecture
2. User generates a share link: https://claude.ai/share/20a6b11e-...
3. User pastes the link into Claude Code: "incorporate this research into our plan"
4. Claude Code tries WebFetch → 403 Forbidden
5. User suggests Playwright MCP → plugin not loaded or also blocked
6. User has to manually copy-paste the content

Why this matters:

Claude.ai and Claude Code are both Anthropic products. Users naturally move between them — research in the conversational UI, implement in the code UI. Shared links are the bridge. Blocking Claude
Code from reading its own platform's shared links creates unnecessary friction in what should be a seamless workflow.

Expected behavior:

Claude Code should be able to read claude.ai/share/* URLs, either via:

• WebFetch recognizing them as same-platform and authenticating
• A dedicated tool/MCP for accessing Claude.ai shared conversations
• The share endpoint returning content without auth (it's a public share link)

Workaround:

User manually copies conversation content and pastes it into the Claude Code session. This works but defeats the purpose of share links.

Environment:

• Claude Code version: 2.1.81
• Platform: macOS Darwin 25.2.0

Environment Info

• Platform: darwin
• Terminal: iTerm.app
• Version: 2.1.81
• Feedback ID: 2c1d79b8-b60f-47ae-924d-48fa820dbe0b

Errors

[{"error":"Error: NON-FATAL: Lock acquisition failed for /Users/jordan_of/.local/share/claude/versions/2.1.81 (expected in multi-process scenarios)\n    at TET (/$bunfs/root/src/entrypoints/cli.js:2724:2174)\n    at fgq (/$bunfs/root/src/entrypoints/cli.js:2724:1318)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T09:08:14.495Z"},{"error":"Error: Plugin MCP server error - mcp-config-invalid: MCP server github invalid: Missing environment variables: GITHUB_PERSONAL_ACCESS_TOKEN\n    at JM_ (/$bunfs/root/src/entrypoints/cli.js:2562:22291)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T09:08:14.517Z"},{"error":"Error: Plugin MCP server error - mcp-config-invalid: MCP server github invalid: Missing environment variables: GITHUB_PERSONAL_ACCESS_TOKEN\n    at JM_ (/$bunfs/root/src/entrypoints/cli.js:2562:22291)\n    at async M (/$bunfs/root/src/entrypoints/cli.js:5348:9913)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T09:08:15.951Z"},{"error":"Error: Plugin MCP server error - mcp-config-invalid: MCP server github invalid: Missing environment variables: GITHUB_PERSONAL_ACCESS_TOKEN\n    at JM_ (/$bunfs/root/src/entrypoints/cli.js:2562:22291)\n    at async G (/$bunfs/root/src/entrypoints/cli.js:5348:10629)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T09:08:15.952Z"},{"error":"Error: File does not exist. Note: your current working directory is /Users/jordan_of/code/monofolk/.worktrees/proto-tooling.\n    at call (/$bunfs/root/src/entrypoints/cli.js:4321:6398)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T15:56:31.414Z"},{"error":"Error: EISDIR: illegal operation on a directory, read '/Users/jordan_of/code/monofolk/.worktrees/proto-tooling/.github'\n    at B$_ (/$bunfs/root/src/entrypoints/cli.js:925:8336)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T15:56:43.834Z"},{"error":"AxiosError: Request failed with status code 403\n    at Uu (/$bunfs/root/src/entrypoints/cli.js:74:1194)\n    at <anonymous> (/$bunfs/root/src/entrypoints/cli.js:79:12762)\n    at emit (node:events:92:22)\n    at endReadableNT (internal:streams/readable:861:50)\n    at processTicksAndRejections (native:7:39)\n    at request (/$bunfs/root/src/entrypoints/cli.js:81:2467)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T16:01:17.570Z"},{"error":"AxiosError: Request failed with status code 403\n    at Uu (/$bunfs/root/src/entrypoints/cli.js:74:1194)\n    at <anonymous> (/$bunfs/root/src/entrypoints/cli.js:79:12762)\n    at emit (node:events:92:22)\n    at endReadableNT (internal:streams/readable:861:50)\n    at processTicksAndRejections (native:7:39)\n    at request (/$bunfs/root/src/entrypoints/cli.js:81:2467)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-03-21T16:23:12.004Z"}]