A Gold Card holder who becomes a lawful permanent resident is subject to the ordinary rules, which reach worldwide income. There is no separate regime attached to the card and no exemption for earnings kept abroad. Confirm with a qualified tax professional how those rules would apply to each of your income sources before committing.
Ask about your structures, not the program
The productive question is not how the Gold Card is taxed but what happens to a holding company, rental income and a pension if the owner becomes a permanent resident. Bring the entity documents and let the adviser work from them. Where an answer depends on a treaty, a filing election or the timing of residence, ask what the alternatives are and what each requires. Generic reassurance is not advice.
As published: a nonrefundable processing fee, successful vetting, and a gift to the U.S. government, after which the applicant proceeds through an existing employment-based immigrant category subject to its own eligibility rules, admissibility and visa availability. Because the case ultimately rests on an existing category, the ordinary conditions of that category continue to apply: admissibility, the medical examination, the security and background review and the availability of a visa number under the visa bulletin.