Network Diagnostics (start here)
Settings > Network > Run Diagnostics. If anything fails (DNS, HTTP, SSL) - that could be the issue. Are you using a VPN, corporate network, or antivirus?
Try disabling HTTP/2
Settings > Network > HTTP Compatibility Mode > HTTP/1.1. This is especially important for corporate networks, VPN, or Zscaler.
Disable all extensions
Run from command line: cursor --disable-extensions. If Chat starts working, then some extension is blocking it. Enable them one by one to find the culprit.
Check indexing
Look at the status bar in the bottom right - is indexing running? A few users had the agent hang because indexing was blocking it. One user fixed it by updating to version .35.
If nothing works, please share the Network Diagnostics results and a screenshot from Developer Tools (Ctrl+Shift+P > Developer: Toggle Developer Tools > Console). Let me know if there are any red errors there.