How/where did you configure the forwarding? By default, Exchange Online blocks forwarding to external addresses, so the first thing to do here is go over this article to cover the basics: https://techcommunity.microsoft.com/t5/exchange-team-blog/all-you-need-to-know-about-automatic-email-forwarding-in/ba-p/2074888
If you are still having issues, run a message trace against one of the failing messages and post the (sanitized) results: https://learn.microsoft.com/en-us/exchange/monitoring/trace-an-email-message/message-trace-modern-eac