How to autoforward emails using an email client when forwarding is prevented in Outlook Web or Gmail?

What are the email web servers, web services, and cloud services you mentioned? In addition, how do you disable auto forwarding?

If you are setting up to block forwarding mail through the exchange server, as far as I know, as an admin, you can use mail flow rules to detect and block automatically forwarded messages to external recipients, or use remote domain to allow or block automatic email forwarding to some or all external domains. Maybe you can find some good suggestions by setting some filtering conditions from these methods:

Mail flow rules (transport rules) in Exchange Online

Remote domains in Exchange Online

If you disable auto forwarding through other methods, such as some gmail settings, it is suggested that you could post in Gmail related forums for more professional help.