TR didn’t want to break up trusts, he wanted the Government to regulate them. He was a Hamiltonian.
This ^^^ is NOT Hamiltonian.
The myth of "hamiltonian" and "jeffersonian" in our modern conception is rooted in Herbert Croly (mentioned above by the original author) in case you want to know where that nonsense originated from.
https://librivox.org/the-promise-of-american-life-herbert-croly/ Audio, or text for reading.
There's several chapters of it there, all of it will be familiar even though you've likely never read or listened to this work. That's because this is where it originates.