Amazon Q chat window does not load anything in code-server (browser client)

## Problem

Amazon Q chat window does not load anything in code-server (browser client). Log in was successful. However, when I open the extension in left side pane, the "chat" window shows nothing inside, just an empty box, no inputs, etc. Did not find interesting logs either. I use it with SSO and logs show authentication successful at us-east-1.

This could be similar to https://github.com/aws/aws-toolkit-vscode/issues/8057.

However, in my case, I am able to load the chat window in my local VS Code installation. The problematic setup is a remote code-server. It uses Nginx for HTTPS support and uses SSH tunneling (dynamic forward) to connect to the remote server.

## Steps to reproduce the issue

1. Install code-server on a remote server.
2. Install Nginx on the remote server and forward 0.0.0.0:8443 to 127.0.0.1:8080.
3. On local desktop, use SSH to create a dynamic forwarding tunnel (-D).
4. On local desktop, in Chrome, use FoxyProxy to set a proxy rule, that the remote host's domain name is forwarded through the dynamic forwarding tunnel port.
5. Open code-server using remote server's domain name and port 8443 in Chrome. Sign in.
6. Install Amazon Q extension.
7. Sign in with company SSO.
8. Open Amazon Q in left side pane.

## Expected behavior

Should show input box and initial prompts in the "chat" window.

However, it shows nothing in the "chat" window.

## System details (run `AWS: About` and/or `Amazon Q: About`)

- OS:
- Local: macOS Tahoe 26.2 (`uname`: 25.2.0)
- Remote: Amazon Linux 2 (`uname`: 5.10.245-245.983.amzn2int.x86_64)
- Visual Studio Code version:
- code-server: v4.106.2
- Code: 1.106.2
- Commit: 904942a1944f66a886b0ec5c0c60f312d559a6e6
- Date: 2025-11-19T23:08:02.570Z (4 wks ago)
- Browser: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/143.0.0.0 Safari/537.36
- AWS Toolkit version: 3.90.0 (disabled)
- Amazon Q version: 1.106.0

Reproduce the issue using the listed code-server, Nginx, SSH dynamic-forwarding, Chrome, and Amazon Q SSO steps, then inspect the browser and extension behavior when the Amazon Q chat pane is opened. Compare the remote browser-client case with the linked AWS Toolkit issue 8057 and the working local VS Code case; done means the chat pane displays its input box and initial prompts.

Written by the indexing model from the issue text.