How can one strengthen faith and correct intention in prayer, especially when in doubt about uttering the Takbir or feeling hypocrisy in congregational prayer?

It is clear that you are afflicted with obsessive thoughts (waswas) regarding the Takbirat al-Ihram. The best way to treat this is to ignore the obsessive thoughts and never repeat them. An individual afflicted with such obsessions may adopt the easiest of opinions until Allah Almighty grants them healing. Among the greatest means that help a servant achieve sincerity is to supplicate to Allah to grant them sincerity, and to have a hidden good deed that they perform secretly between themselves and Allah. We advise you to adhere to supplication and humble entreaty, to ignore these obsessive thoughts, and to consult a trustworthy psychiatrist.