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This isn’t really a question about JSON.
Surely the token is associated with a user ID? I don’t use django-rest-framework, but the documentation for TokenAuthentication is pretty clear that once the user logs in with their token, you’ll get a normal auth.User instance in request.user just like you would with a standard web-based login.
Your second question is probably made irrelevant by that, but even so, you can always query by an email address, without needing to loop through:
Manager.objects.get(email=my_email_address)
Again this is standard Django querying – if you’re not familiar with that syntax, you should do the Django tutorial.
Of course, since you have a User already, you can do a more efficient foreign key lookup:
Manager.objects.get(user=request.user)
or even
request.user.manager
(assuming you have a one-to-one relationship from User to Manager – it would have been helpful to see your models).