Demystifying Hybrid Free/Busy: Finding errors and troubleshooting

C-Money The errors are network related, so if you want to make sure the Faulty Request didn't reach Exchange server on-premises, check IIS, HTTPProxy logs for Autodiscover. Based on the error, I wouldn't expect to see it all in that HH:MM:SS when you query the f/b. Or if you see it, with a 200 OK request, check maybe the Time-Taken in IIS logs and see if that is causing the connection timeout.  Compare with the working request. See above how to analyze those logs. If you have multiple servers, make sure they are not in maintenance, or if they are, they should have ServerWideOffline on in Get-ServerComponentState.
Make sure there is really no connection filtering set, and double check row 1 from this article is whitelisted. Office 365 URLs and IP address ranges - Microsoft 365 Enterprise | Microsoft Learn

If you have Load Balancers, make sure they are working as expected, you can also point them to one Exchange server and see if this fixes the problem. 

Also, you can check TLS related stuff and Load balancing health probably with HealthChecker - Microsoft - CSS-Exchange