The federal government doesn’t outlaw abortion, so they can’t use the Commerce Clause to enforce abortion restrictions enacted by the states.
However, the issues you cite with them being bullies with the commerce clause are centered on authority granted through Gibbons.
Gibbons was specifically about states trying to enforce laws (specifically state-granted steamboat monopolies) within their borders that had a direct impact on commerce within another state. The Supreme Court declared that a violation of the commerce clause because only the Federal Government can regulate interstate commerce.
Texas passing laws prohibiting travel to another state to seek abortions (which are federally legal) could only be allowed by SCOTUS by overturning Gibbons, which would be absolutely devastating.
That would be by far the most-impactful reversal in the Court’s history, and it can’t be overstated how much of a grenade it would be. Everybody would lose, and the GOP’s owners more than anyone else.