The FAA does have licenses over launch and they are trying to impose rules for upper stages of launch vehicles [0]. The FAA said they would complete these regulations in 2025 [1], but I haven't seen something saying they have gone in to effect yet.

The FCC does deal with disposal requirements for US satellites that are launched. In order to secure a license from the FCC you have to prove that your satellite will meet the latest guideline that it will be disposed of (either de-orbit for LEO, or moved to disposal orbit for higher orbits) within 5 years after mission complete [2]. Unfortunately this doesn't seem to apply to upper stages for some reason even though I would say that it is an orbit object that gets licensed and would "complete the mission" after deploying the satellites and have to abide by the 5 year rule.

[0] https://www.faa.gov/newsroom/faa-proposed-rule-would-reduce-...

[1] https://spacenews.com/faa-to-complete-orbital-debris-upper-s...

[2] https://www.fcc.gov/space/faq-orbital-debris

It is the FCC[1]. The FAA is only concerned about the launch and de-orbiting as it passes through airspace, and doesn't regulate what happens between, including whether object de-orbit at all. It is odd for the FCC to have this responsibility. They kind of picked it up by default since they were the only agency regulating operations in space in any way, and we had ratified treaties that needed to be enforced, without creating an agency to enforce them.

Edit: The FAA is also proposing orbital debris rules that were supposed to be finalized this year, but aren't released yet[2]. This whole area is a mess, and really needs congress to set clear responsibilities.

[1] https://www.fcc.gov/space/orbital-debris

[2] https://spacenews.com/faa-to-complete-orbital-debris-upper-s...

For the actual current rules about collisions and debris broadly see: https://www.ecfr.gov/current/title-47/chapter-I/subchapter-B...