The anti-abortion movement has always had authoritarian underpinnings; forcing women to give birth against their will would require police-state surveillance and coercion. (It’s certainly more intrusive than being made to wear a mask, which some conservatives regard as tyranny.)
The anti-abortion movement is not merely authoritarian and intrusive; it is misleading. Definitely, it doesn’t mean to rest with the end of Roe. Albert Mohler, for instance, has made it clear through the years that he wants to eliminate the availability of birth control, too.