If you look at the text of the bill, the authors have included multiple severability clauses. I think they have one for literally each subject. I think Democrats are being a lot more careful with major legislation nowadays considering what nearly happened to the ACA in 2012 (specifically in terms of severability and the fact that the dissent wanted to strike down the entire law).
I do wish the legislation had fallback options that became operative if others were struck down. I especially look at the redistricting provisions for that. That is the most important part of this legislation. I think the fallback option should be either a federal redistricting commission (with strict guidelines as to who would be qualified) and/or very strict criteria as to what is allowed and disallowed. Part of the problem with the VRA (particularly Section 5) is that it only applied to certain states. Section 5 wasn't struck down though. It was the coverage formula under Section 4 that was held to be unconstitutional. I would prefer an attempt to put all 50 states under Section 5 preclearance.
To clarify for everybody, there are no provisions of H.R. 1 (at least, as far as I can tell) that seek to implement limitations on anything - incl. partisan gerrymandering - at the state legislative &/or local level. Doing so would be unconstitutional, yes, which is why the bill's provisions only require states to use independent commissions for congressional district lines.
I'm fairly sure the VRA's redistricting provisions also apply to state and local government. However, that would not seem to be a power of the Elections Clause, but rather a power under the Fifteenth Amendment's enforcement clause. I think Congress probably has some limited power to set some standards even for state and local government.
