Claude in Chrome: per-domain permission has no prompt or settings surface, silently blocks all access

**Environment**
- Claude Code desktop app (macOS)
- Tool: mcp__claude-in-chrome__* (Browser pane / "Claude in Chrome")

**What happened**
Any action on a specific domain (app.qbo.intuit.com, az.cwa.sellercloud.com) fails with:
- `Permission denied for this action on this domain` (from `computer`/screenshot)
- `Permission denied for reading pages on this domain` (from `read_page`)

`navigate` itself succeeds (the tab loads and shows the correct page title/URL), but every
subsequent interaction on that tab is denied. This happened both in an unattended scheduled
task run and in a live interactive session with the user watching the Chrome window the whole
time — no permission prompt, popup, or notification ever appeared for the user to approve.

**What I expected**
Either:
1. An on-demand approval prompt surfaces in Chrome (or the Claude Code app) the first time a
new domain is touched, which the user can click through, or
2. A settings/allowlist surface exists somewhere the user can proactively grant domains before
running a task (especially important for unattended scheduled tasks, which can never resolve
an in-the-moment prompt).

Neither exists as far as we could find.

**Diagnostics performed to rule out other causes**
- No MDM enrollment: `profiles status` → "There are no configuration profiles installed on
this system"; `/Library/Managed Preferences/` doesn't exist.
- No Chrome enterprise policy directories under
`/Library/Application Support/Google/Chrome/`.
- No trace of a Claude/Anthropic extension anywhere in Chrome's own `Local State` file —
suggesting "Claude in Chrome" isn't a conventional installed Chrome extension, or at least
isn't discoverable that way.
- Claude Code's own permission settings (`~/.claude/settings.json`,
project `.claude/settings.local.json`) already list the `mcp__claude-in-chrome__*` tools as
broadly allowed, unscoped by domain — so it isn't Claude Code's local tool-permission system
blocking it.
- The org's signed policy file (`policy-limits.json`) only carries three unrelated flags
(`allow_remote_control`, `allow_quick_web_setup`, `enforce_web_search_mcp_isolation`) —
nothing about domain-scoped browsing.

So the gate appears to live inside the "Claude in Chrome" service's own runtime, with no
externally visible prompt, log, or settings surface.

**Impact**
- Blocks a scheduled/unattended task (a weekly accounts-payable sweep) from ever completing the
portion of its work that depends on those domains — it fails identically every run with no
way to pre-authorize.
- Blocks interactive use too, since no prompt ever surfaces even when the user is actively
watching the browser pane.

**Ask**
Please expose either an on-demand approval prompt or a persistent settings/allowlist for
per-domain "Claude in Chrome" access, and/or document where this gate actually lives if one of
these already exists and we simply couldn't find it.

Start by tracing the mcp__claude-in-chrome__* tools and the reported permission-denied responses; the issue does not identify a repository file or implementation entry point. Review the referenced ~/.claude/settings.json, project .claude/settings.local.json, and policy-limits.json only to confirm those surfaces do not control domain access. Done means defining and implementing an approved prompt or allowlist surface, or documenting the existing one.

Written by the indexing model from the issue text.