yup. that was the big ramification of planned parenthood v casey in the late 90's. after roe v wade, they used the trimester system... as in during the first trimester, it was nearly impossible to restrict abortion, and in the third trimester, state could basically do whatever it wanted, and 2nd trimester was the gray area.
after Casey, they scrapped that and instead looked at pre and post viability. and yes, as medicine/technology progresses, viability gets pushed closer and closer to conception.
it's not that they "can't restrict" but any restriction would face strict scrutiny. basically the state would need to show that the restriction is necessary to further a compelling state interest. which effectively means they cant barring something extraordinary. this is what is referred to as strict scrutiny. there's an expression that goes "strict in theory, fatal in fact" which means "strict scrutiny" is basically legal code for "you cant touch it"
i'm not sure exactly what week it is... and i dont think its really a bright line of how many weeks. its more of a case by case basis where the doctor determines the viability at that point.
but the general rule would be:
before viability, there is a cons utionally protected right to have an abortion, which states cant infringe on (rationale being at that point, the mother's interest of privacy/choice outweigh the state's interest in preserving the potential life)
after viability, states can pass restrictions, as the cons utional protections are much weaker here.
overturning roe would basically scrap the entire notion of a cons utionally protected right to have an abortion at any stage, which would open the door for states to pass complete bans. but even then, states like CA or NY will still allow abortions. the misconception is that overturning roe = outlawing abortion federally