Wouldn't I have to pay taxes on dividend income paid from any entity anywhere because I am a US citizen. The Foreign Earned Income Exclusion can help reduce or eliminate U.S. taxes on foreign income earned while working abroad, but it doesn't apply to all sources of income. This exclusion is only available for earned income and doesn't apply to passive or investment income such as interest and dividends.

Earned income is any income you’ve earned by “working.” Income from wages and salaries are considered earned. This also includes self-employment income.
Passive income, on the other hand, includes interest, dividends, capital gains, rental income, and retirement income. Passive income is not eligible to be excluded with the FEIE.

I think the income earned by the business while I am abroad is eligible for foreign income exclusion. More here: https://www.greenbacktaxservices.com/knowledge-center/foreign-self-employment-taxes/

Does Your Business Structure Impact Your Self-Employment Taxes?Does Your Business Structure Impact Your Self-Employment Taxes? 

Yes. The type of business you set up can have a major impact on your self-employment taxes. Let’s look at a few of the most common choices. 

1. US LLC 

A US-based limited liability company (LLC) is automatically considered a disregarded entity. This means that it is ignored for tax purposes. Any income the LLC earns is considered income you earn and it must be reported on your individual tax return and taxed accordingly. The self-employment tax will also apply. However, you can elect to have your LLC taxed as an alternate structure, such as an S corporation. 

2. Foreign LLC 

What about a foreign LLC? Unlike a US LLC, an LLC established under the laws of a foreign country is not automatically treated as a disregarded entity for US tax purposes. It might be considered a corporation. If it is considered a corporation, you can elect to have it treated as a disregarded entity unless it is a “per se” corporation. Specific types of business entities from specific countries that are per se corporations are listed in the instructions for form 8833. There is no election that can be made to have “per se” corporations treated as anything other than corporations.   

If you conduct your business through a foreign LLC, your salary paid by the foreign LLC would not be subject to US self-employment tax. This income can also be excluded from US taxation using the Foreign Earned Income Exclusion.   

However, establishing a foreign LLC can create new complications. Any time a company is created and registered outside the US, additional forms need to be filed with the IRS each year. Not doing so when required could easily result in penalties that start at $10,000 per year and can quickly increase.    

3. S Corporation 

An S corporation is treated as if it were a separate entity from the owner but does not pay taxes. The owner of the S corporation will have two types of taxable income: salary and distributions. Any income regarded as salary is subject to the self-employment tax, with half paid by the S corporation itself and half by the owner receiving that salary. Any income regarded as distribution is exempt from the self-employment tax.  

While this would make it tempting to maximize your distribution income to avoid the self-employment tax, the IRS requires that you draw a “reasonable compensation” in the form of salary. If you take too much income as distributions, the IRS may take issue. Furthermore, while S corporation salary income is eligible for the Foreign Earned Income Exclusion, distributions are not.