In the UK:
Your company pays corporation tax based on profits during the tax year. Whatever money is left can be disbursed to employees, shareholders, etc.
You as an individual pay tax based on your yearly income. There are several tax brackets depending on how much you make, as well as "free" brackets (you don't pay anything on the first ~12k of employment income, and there's an equivalent for dividends but much smaller).
Anything you pay yourself from your company then incurs this individual-level taxation, but since you can choose how much you pay yourself you can only pay the minimum (to stay within "acceptable" tax brackets) and keep the rest in the company for next year or for company-level investments (new hardware, expanding the business, etc). For limited-company contractors, the usual strategy is to pay yourself ~12k/year of salary and the rest is in the form of dividends which you can vary depending on your situation & needs.
Is it complex to manage? Depends on the jurisdiction; some are more evolved than others. In the UK I find it super easy and while I can bitch all day about the amount of tax I'm paying, at least the documentation is quite clear and they make it super easy to manage everything. I do have an accountant but at this point it's mostly for advice and "just in case" than anything else - day to day is handled by FreeAgent and I just have to make sure the data is entered properly and the software takes care of the rest.
Companies that have an urgent need for a certain skill will be happy to take you on as a freelancer for higher money, either while they look for permanent staff or if it's just a one-off bet and they're not yet sure whether it's worth getting permanent resource for something that may be discontinued. Get a steady stream of these gigs for a year and you make twice the money you'd make as a permanent (outside FAANG maybe), and if you keep your burn rate low you can also leave the bulk of the money in the company for the next tax year and take advantage of the lower tax brackets which you can't do as a permanent employee.
Regarding the $1/hour MVP, that's just down to where you find your gigs. I recommend getting your gigs either directly via your network, or failing that, via recruiters - yes they take a cut and they might be shit but there's also good ones (see https://news.ycombinator.com/item?id=29392115) - in my experience good old "brick & mortar" (well, not so much during the pandemic but you see what I mean) recruiters have a barrier to entry that's very effective at keeping "$1/hour millionaire-maker SaaS" at bay, which also helps with regards to getting paid as what's left is typically established businesses within your own country and in reach of the legal system you have access to.
Absolutely do not waste your time on Upwork or similar - that's the bottom of the barrel where $1/hour MVP is commonplace in a self-reinforcing feedback loop, as good talent leaves which means good projects also leave and the only thing remaining is crap - on both sides of the market that is.