Yes it does: the Federal government currently allows states to choose between permanent Standard Time and Standard/Daylight switch at the point specified in federal law, it also dictates the timezones in the US and their boundaries. So, e.g., California has a choice between permanent PST and PST/PDT switches (it has chosen the latter), and Arizona between permanent MST and MST/MDT switches (they’ve chosen the former).
If the feds get rid of the option for DST switching and the option to chose permanent standard time in favor of mandating permanent daylight time with no other options, then, yes, the states have to do it.
Now, if they replace the daylight switch option with a permanent daylight option, that would be a different story. And if they just added a permanent daylight option, that would be an even more different story. And the text isn’t up for HR 69. But I suspect its straight “permanent DST is the only option” rule.
States can choose to stay on Standard, or go back and forth, but currently they can't choose to stay on DST. I think WA, OR, and CA have all passed legislation that would move them over once the feds allow it.