I strongly advise you to map the form to a class and create a custom constraint...
I have written a detailed example on how to:
- create your own validation constraint
- turn it into a service
- inject the object-manager
- access the database from the constraint
TLDR:
What you need is a custom validator on class level.
A class-level validator is needed because you need to access the whole object (not only a single property) if you want validate multiple related values...
... or need to fetch something from database using another property as select-criteria.
Here's the the complete answer with example.
Another option could be creating a form-event listener and passing the object-manager to it before adding it to the form.
Then take care of the validation-process (checking the data against the database + eventually adding errors to the form) inside the listener yourself.