Your question has no simple answer because Pai's reasoning is based on suspect premises.
The California bill merely controls which vendors that the State of California can purchases services from. This type of regulation is premised on a long-established limitation on the extent of Federal powers; namely, that the Federal Government has no power to directly regulate State policies, and in particular its choice of vendors. The logic is that a State is a sovereign political entity, and sovereignty means that there must be a bright line somewhere where the State is completely independent.
As that line stands today, the vast majority of legal scholars would tell you that California is well within its rights to control the contractual terms with its vendors, free from Federal constraints.[1] In fact, the original bill was pulled and amended so ensure it fit squarely within these allowances. (At least, that's the story of the committee members who delayed it.) The closest SCOTUS has allowed the Federal government to control contractual policies of the State involved employment, where SCOTUS permitted enforcement of the Fair Labor Standards Act against State government employers. But it was a close call, most of the conservatives were in dissent, and almost all conservatives have subsequently at least paid lip-service to criticisms of that decision.
That said, there may be strong legal arguments that permit the Federal government to interpose themselves between the State and municipalities without moving that bright line. There are many ways to distinguish and distance municipalities from the State itself.
Also, it's becoming difficult to deny at this point that as conservatives have come to dominate the Federal government, conservative policy arguments have become increasingly supportive of stronger Federal regulatory powers. It's excused as a necessary evil for defending laissez faire economic principles[2], but that's just face-saving. And these arguments are being adopted by conservatives across the spectrum, including (and especially?) among jurists.
[1] At least constraints flowing from Commerce Clause powers. Constraints flowing from the 14th Amendment are a different matter because the 14th Amendment imposes explicit limitations on States and explicitly gives Congress legislative powers to enforce those limitations. But even then there's a bright line Congress cannot cross, albeit a more narrowly circumscribed line.
[2] And don't even get me started on the fact that Net Neutrality is, IMHO, a very pro free market policy. It's no more restrictive of a "free market" than are crimes prohibiting fraud. There comes a point at which one's freedom impinges upon the freedom of others to the extent that there's a net loss of economic freedom. Furthermore, there are many examples of market legislation intended to overcome transactional inefficiencies that inhibit or prevent markets from reaching more optimal outcomes. Its why we even have laws at all, rather than relying upon everybody to explicitly contract with everybody else for every little interaction.