UPDATE: April 2026. To this date, we have found that New Outlook is not working reliably with Google Workspace - in particular with synconising after moving or filing mail. So it is our recommendation to not use New Outlook - you could lose emails!
For New Outlook Desktop (2025) App to work with Google Workspace accounts, you'll need to change a setting in your Google Workspace GMail account...
Gmail > Settings Cog -> See Allsettings -> Forwarding and Pop/IMAP -> Auto-Expunge On.
If you don't do this setting, Outlook and GMail won't syncronise properly. If you move an email in Outlook, it will look like it worked in Outlook... but Gmail will show no change!