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The branches are explicitly defined in the Constitution.
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What we consider an the branches are defined in the Constitution, but my point is they are not simply defined as the top-level in a hierarchy of organizations, but rather behaviorally based on what function is being performed.
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> What exactly makes the GAO not "part of the executive branch" ?

https://www.law.cornell.edu/uscode/text/31/702

>> (a)The Government Accountability Office is an instrumentality of the United States Government independent of the executive departments.

The law establishing it also establishes it as independent.

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Sure, that is what is written down. But as a necessary part of its operation, there is a whole lot of executive power being exercised as well, which the unitary executive theory says would fall under the authority of the president.
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