You don't have to. If it becomes capital, then it is subject to the same multi-stakeholder analysis.
If I bought a printer, it would just be a commodity. If I start selling products made from said printer and hire more people, then it would need to be a worker coöp.
How would an authoritarian socialist system handle someone wanting a printer given that it could be used as capital?
*Capital markets. Commodity markets are fine as long as you align stakeholders with ownership. So worker and consumer coöps. Rental and housing coöps are a great example.
I like to take a Mutualist position on it. Things should only be socialized to their direct stakeholders. So most companies would be worker coöps. Utilities would be consumer worker coöps. And large interstate transit would be federal. Universal healthcare would fall into the later as a largescale consumer coöp.
I'd argue if Trump gets his way and becomes dictator for life. That's more right authoritarian than left authoritarian.
As a Mutualist, I firmly disagree. Coöps are essentially a democratic alternative to top-down coercive management styles or forms of ownership. It is a mutualist system that is antithetical to competition.
Take a renter's coöp for example. Essentially everyone owns their building and they aren't competing with other buildings or have shareholders would expect a return on investment.
With coöps you can actually respect locality. Large auth-socialist systems will often have with people competing interests who have undo control over local systems. That isn't to say broader standards shouldn't exist, but that they should be done thru voluntary industry wide syndication.