Dear Stuart Bray1
Greetings!
Thank you for posting on Microsoft Community!
Based on your description, I understand your query about searching the Online Archive in Outlook for Mac.
According to investigation and tests on my end, while in New Outlook for Mac you can search the Online Archive folder directly with no problem (like in OWA), it seems in Legacy Outlook for Mac you can only search mails in online archive folder by selecting Current Folder option when searching. So would you please kindly try switching to the new Outlook for Mac or searching like in below screenshot?
Thank you in advance for your understanding! Your patience and cooperation will be greatly appreciated. I hope all the best!