To use gmail, you'd need to update your MX (Mail Exchanger) records in the DNS for your domain. You'll need to get the correct MX records for gmail from Google, then update the records to point to their mail servers. Hopefully the following help article will be of use:
I'm also trying to link mulitiple Workspace Webmails with a gmail account so I can check them off site. When I tried to set up I got everything in my gmail account but then all old messages disappeared from the Webmail accounts. Any idea how to get them back? Our admin needs to have access on her computer too.