Engineering manager to TPM?

At bloomberg currently, we don't have TPMs. I became a TL (Bloomberg speak for first level EM) to have more control over product direction, lead people, and stay somewhat technical. This sounds similar to me as a TPM role at F/G (and I'm sure other places).. Am I along the right lines? Do these companies hire TPMs from ICs/EMs? Is TC comparable (250k/6 YOE)