I don't think you're breaking the single responsibility rule by including the checks within your ContactMailer
class. It would have the single responsibility of sending the mail if the project meets certain conditions.
A class with a single method isn't necessarily overkill, and there may be good reasons for abstracting the check logic into a separate class which aren't apparent to me from your question. However, from what you've said, I think your architecture sounds absolutely fine.
Just as an aside, if you did separate the check logic into a separate class, what would you call the class? MailConditionsChecker
? In my experience, it's generally a bad sign if it's difficult to come up with a sensible noun to name your class.