Chrome extension: 'Browser URL could not be parsed' on subdomain URLs (brain.fountain-city.com)

Bug Description

The Claude Code Chrome extension (Cowork) fails to use any interactive browser tools on pages served from a subdomain URL. Every tool returns the same error: "Browser URL could not be parsed".

Steps to Reproduce

1. Navigate to https://brain.fountain-city.com/ (or any path on that domain) in Chrome
2. Open Claude Code in Cowork mode
3. Attempt any interactive tool (screenshot, click, read page content, etc.)
4. All tools return: Browser URL could not be parsed

Expected Behavior

Interactive tools should work on subdomain URLs the same as on root domains.

Actual Behavior

Every interactive tool fails with the URL parsing error. The error is consistent across all pages and paths on the domain. The site loads normally in the browser — only the extension's tools fail.

Environment

• Claude Code CLI: OpenClaw-based (latest stable)
• Chrome extension: Claude in Chrome (latest from Chrome Web Store)
• Browser: Chrome (latest stable)
• OS: Linux (Ubuntu on AWS EC2)
• Domain: brain.fountain-city.com (subdomain of fountain-city.com)
• Site stack: Express.js + HTTPS (Cloudflare origin cert), behind Cloudflare proxy

What I've Tried

• Relaxed CSP headers to allow Chrome extension interaction (unsafe-eval, unsafe-inline, chrome-extension: in connect-src, disabled crossOriginOpenerPolicy and crossOriginResourcePolicy)
• Verified the domain is explicitly allowed in extension permissions
• Confirmed the site works fine in the browser (loads, authenticates, all features work)
• Tested multiple pages/paths on the same domain — all fail identically

Hypothesis

The extension's URL parser may not handle subdomain formats correctly. The domain brain.fountain-city.com has a subdomain (brain) on a hyphenated second-level domain (fountain-city), which may trip up URL parsing logic that assumes simpler domain structures.

Related Issues

• #39956 (.tech TLD issue — different bug, same user, different domain)
• #15260 (wildcard subdomain matching)
• #29057 (Chrome extension connection failures)

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