Thank you!

I found exactly what I was looking for (it was really hard to find): IRS Pub 541, bold/italics by me:

Publication 541 (03/2021), Partnerships

Community property.

Spouses who own a qualified entity (defined below) can choose to classify the entity as a partnership for federal tax purposes by filing the appropriate partnership tax returns. They can choose to classify the entity as a sole proprietorship by filing a Schedule C (Form 1040) listing one spouse as the sole proprietor. A change in reporting position will be treated for federal tax purposes as a conversion of the entity.

A qualified entity is a business entity that meets all the following requirements.

• The business entity is wholly owned by spouses as community property under the laws of a state, a foreign country, or a possession of the United States.
• No person other than one or both spouses would be considered an owner for federal tax purposes.
• The business entity is not treated as a corporation.

For more information about community property, see Pub. 555, Community Property. Pub. 555 discusses the community property laws of Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, and Wisconsin.

To summarize:

I think both alternatives are possible in a community property state: you can 1) split the Schedule Cs and the Schedule SEs between husband wife or you can ( 2 Cs, 2 SEs) 2) assign the husband-wife LLC to one spouse as the sole owner -> 1 Schedule C in the name of that owner and 1 Schedule SE in the name of that owner.

2) is beneficial for low SE incomes, since it allows you to aggregate the income from both spouses which allows you to take higher deductions against it (like health insurance).

But once you assign to one owner, I guess it has to stay that way.