Does open source software hinder competition?

For closed source software, every software has its secrets, and these secrets are a means of competition.

But if everything is open source, then this reinforces monopoly by making it so that the more established software can just copy the code of the underdog's software that works better, and now the established software has benefits of both reputation and code that works, and no one is left with any reason to use the underdog's software.

This used to be true in the past.  In the past, it made sense to make tools open source and make applications proprietary.  But these days it no longer matters since all modern scum are revolted by good code and wouldn't use it anyway.

Yeah but they can still benefit from the code being open source in other ways. For example, at my last workplace, I made a software that was a threat to the modern scums' software. People were using my software, and it worked well, and it even compensated for memory leaks that existed in the modern scums' software, and therefore the modern scum had no means to attack it. Then the modern scum forced me to make my software open source. And after I made it open source they did an attack on the way my software was written. They said my software wasn't testable because it wasn't written with the model-view-controller, and management forced me to discontinue. By making my software open source, they were able to improve their relative reputation by attacking mine. I guess the general idea is information seems to benefit the establishment more than the underdog.

That is possible but that is a different argument from your initial post.  In my businesses, I keep everything internal private, not just the code.  This includes my name, of course.