The original AP1 autosteer release (7.0) only had nags under certain road conditions where the system had lower confidence, and during tighter turns. There were no nags based on elapsed time.
Since then, the following restrictions were added in various software releases. This may not be a complete list, and they're in rough chronological order based on my memory:
- Driver's seat must be occupied with seat belt fastened. (Added in a later 7.0 release).
- Nags based on elapsed time (3:00 minutes when not following another car above 45 MPH, 5:00 minutes when following another car over 45 MPH, no elapsed time nags when below 45 MPH) (added in 7.1)
- Speed restricted to speed limit + 5 MPH on undivided roads (added around 8.0).
- Timed nags below 45 MPH, around 10:00 minutes. (Added 8.1).
- Progressive warnings (Hold Steering Wheel Alert -> IC Flashing -> Audible Beeps -> Take Over Immediately) added. (Added 8.1)
- Autosteer lockout for remainder of drive if progressive warnings get to Audible Beep level 3 times. (Added 8.1)
- Hold Steering Wheel alerts immediately if accelerator pressed while on autosteer. (Added 8.1)
- Autosteer lockout for remainder of drive if speed exceeds 90 MPH while on autosteer. (Added 8.1).
In answer to the OP's original question, no, there are no laws at either the federal or state level requiring any of these implementations. However, the NHTSA, who was the investigating body during the Joshua Brown fatality incident, has/had the power to force Tesla to change the system or disable it altogether. Most of the restrictions added in the 8.0 and following releases were in response to the NHTSA's investigation and Tesla's desire to keep the NHTSA from taking forceful action.