One option is to have a button on the start page to ask the user to which tenant they belong to, and then authenticate them appropriately. Very little friction in the authentication process: Like are you an employee or a contractor?

Azure has an another option called B2C tenant (they're renaming it now something like Entra External ID or something similar) which is designed to work as user database for things like customers/clients. Instead of developing your own classic MySQL + $whatever framework for authentication to use this service as an alternative.

If you invite an external user that already exists in another Microsoft Azure tenant, you only know their user principal and first/last name. Nothing else. All other info does not get populated into your tenant even if it exists in the source tenant.