Does our constitutional republic promote or restrict economic freedom?

Compared to what?

Compared to some idealized perfect system of maximal economic freedom, obviously any real-world government is not going to match up. There are taxes, of course, but also a huge quantity of regulations, many of which are clearly overcomplicated or unnecessary. Particularly damaging in my opinion are immigration restrictions and tariffs, as these restrict the flow of people and goods across borders which is the fundamental basis of trade. Many taxes and subsidies are also misaligned with the true externalities they are supposed to reflect (agricultural subsidies are too high, while renewable energy subsidies are too low), and while some degree of labor and environmental regulations are necessary they are often too strict or not structured well.

However, if you compare them to dictatorship, constitutional republics do spectacularly well at promoting economic freedom (as well as other forms of liberty). Instead of micromanaging everyone's lives, they give people freedom to live and work as they choose. Compare the US to North Korea (or even South Korea to North Korea!) and the difference could hardly be starker: In North Korea, almost everything you do is controlled by the government, and you have basically no liberty, economic or otherwise. In the US, there are certain rules you have to follow and you've got to pay your taxes, but mostly you get left alone.

What about the other end of the spectrum? Is a constitutional republic more free than anarchy? In a real sense, yes---because anarchy is unstable. In the absence of a strong government, a power vacuum emerges where individuals, corporations, or other special interests can use force and fraud to take advantage of others. We saw this happen in Somalia when their government collapsed; this didn't usher in an era of freedom, but rather allowed warlords to emerge and form new de facto governments every bit as violent and oppressive as the formal government that preceded them.

Indeed, as a matter of real empirical data, constitutional republics such as the US and France, along with constitutional monarchies such as the UK and Norway, are always at the very top of the rankings in terms of economic freedom. No country is perfect, but some are much better than others, and the better ones are almost always constitutional republics or constitutional monarchies.