On what basis could the US federal government encode Roe v. Wade? [closed]

There are proposals to pass a federal law allowing abortion in all states, in case Roe v. Wade is overturned. Ignoring the political feasibility of passing such a law, on what constitutional basis can the federal government regulate abortion?

Previous laws like the Partial-Birth Abortion Ban Act seem to rely on the Commerce Clause, as the wording is (emphasis mine):

Any physician who, in or affecting interstate or foreign commerce, knowingly performs a partial-birth abortion (...) shall be fined under this title or imprisoned not more than 2 years (...)

But abortions seem like they are usually local affairs, so if prosecution must show an effect on interstate commerce, it sounds like such a law may not be very effective.

Is the Commerce Clause also the most likely basis for the federal government to ban states from restricting abortions? How effective is it likely to be? Are there other powers the federal government could use to guarantee the availability of abortions?