[BUG] Org repos not visible in Claude Code web/desktop repo picker despite valid gh token and SSO authorization

Repositories from my organization TGB-Digital do not appear in the Claude Code repo picker (Desktop and claude.ai/code), while every check on the GitHub side passes.

**GitHub username:** gustavojcorreia
**Organization:** TGB-Digital
**Claude Code version:** 2.1.239 (native install, macOS)

**What I verified:**
- `gh repo list TGB-Digital --limit 100` returns all 4 repositories
- `gh auth status`: logged in as gustavojcorreia, scopes `gist`, `read:org`, `repo`, `workflow`
- GitHub CLI is SSO-authorized for TGB-Digital
- `/web-setup` reports `Connected as gustavojcorreia` (ran it multiple times)
- Fully quit and reopened the Desktop app after each attempt
- Reinstalled Claude Code from scratch via the native installer

**Expected:** repositories the connected GitHub account can see should appear in the picker.

**Actual:** the picker shows a stale list. TGB-Digital repositories never appear, including via the search field.

This matches the backend repository indexing issue reported in #57161, #60493 and #79353.

**Request:** please trigger a backend repository index reset for GitHub user gustavojcorreia.

Start by reproducing the picker behavior in Claude Code web/Desktop and compare it with `gh repo list TGB-Digital --limit 100` and `/web-setup`. No source file or test is named; done means the TGB-Digital repositories appear in the picker for the connected GitHub account.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.