I have Office 365 registered with a hotmail home email, and several different work email Teams accounts, and cannot get Teams in Outlook. It is always a struggle to use Teams.
When starting Teams on the Mac I can't log in with my Microsoft account (hotmail), as it is a Personal account, so I never get Teams while using Office as it says "You can't sign in here with a personal account. Use your work or school account instead".
But I have three separate work emails for difference contracts, and I am using Office with my own personal licence, so they don't integrate and I can't use Teams.
I would suggest in your situation I would be wanting to book meetings using the accounts provided by each customer, that way the appointment, meeting etc stays within their tenant and control. I would use three browser profiles to log into Teams for each client, and then book meeting from the calendar there. By all means have all these accounts sync back to Outlook for Mac so you can see them all together.