The Democratic People's™ Republic of Tankiejerk

That’s fair, but if the workers regulate the companies, control supply via subsidies and taxation, and cap the wealth of the investors then doesn’t it have the exact same effect as if a government office made all the business decisions while also allotting the freedom of the workers to create or retire businesses?

Not really - I feel like I should address this in parts, though it's all one statement and I feel like it needed to be denied as a whole statement first.

That’s fair, but if the workers regulate the companies, control supply via subsidies and taxation, and cap the wealth of the investors

This is the ideal functioning of a social democratic welfare state. We... do not really have a fully ideally functioning social democratic welfare state right now (speaking even outside of the US, because we're pretty fucked here), but this is a fundamentally good, or at least better, goal to aim for than our current situation.

then doesn’t it have the exact same effect as if a government office made all the business decisions

No, it does not. What you've proposed, as a social democratic welfare state, results in a government which restricts and encourages economic decisions which it believes will be in the best interest of the workers. The final decision-making power resides with independent firms mostly run by capitalist investors, even if their decisions are restricted by regulations, and invariably, the decision made within those restrictions will be the one which most benefits (or which the investors perceive as most-benefitting) the capitalist investors, not the workers, and not the firm.

What you describe is probably most comparable to French dirigisme

while also allotting the freedom of the workers to create or retire businesses?

This is a common misconception about socialism, or at least many forms of socialism. Under socialism, a worker running a business is not necessarily restricted - what is restricted is who, beyond the worker, can create or retire a business.

Under the loosest definition of socialism, or, if one prefers the more stringent definition of socialism as beyond simply modernist anti-capitalism, under generally anti-capitalist ideals, there is nothing preventing a worker from starting a business and selling their labor.

Where things get fuzzy is ownership of capital. The strictest socialists would say that all ownership of capital is anti-socialist - down to tools being communally shared. This is an extreme position, however. Most socialists accept that some amount of workers owning the tools they themselves use (or, for some who are insistent about ownership being verboten, workers having 'exclusive rights to dictate the usage of their tools as long as the tools are in use by them') is acceptable - what is important is that capital is not a tool to leverage control over others, but a tool to enable one's own labor.

At its absolute loosest, a generalized anti-capitalism, a worker would be able to run a business, hire workers, buy and sell capital on behalf of the firm, etc, in a mostly recognizable way, even if his work was done on what we might regard as an executive level. The difference would be that the capital would belong to the firm he ran - the worker could not simply cash out and leave the other workers high and dry because it's 'his' business. Nor would there be outside non-worker investors.

This is considered by many socialists to be insufficient to qualify as socialism, and many would insist further that a firm must include workers as a fundamental and major part of the decision-making process to be socialists - but even then, again, nothing in most of these conceptions stops a worker from starting a business and hiring workers. It's simply that once other workers are involved, they must be involved in decision-making, in some form - whether by electing who runs the firm, or by worker-investor schemes, or by votes on major decisions.

There are a lot of conceptions of socialism out there, and a lot of different proposals for what we should be working for. About the only point of agreement is that capitalism is not the way forward - that investor-driven market economies have results which follow the iron law of institutions - decisions benefit the decision-makers, not the firms, and certainly not the workers.