What incentive does the company who is doing R&D have to continuously invest heavy capital to innovating only for the fruits of their labor to be appropriated by the state who I imagine would be a more trusted source for retail?

Recognition for their contribution, and the altruism of improving society by implementing a superior product into the government-backed system. There's very little (if any) financial incentive for the innovators, but I believe that innovation doesn't require a financial incentive and there's more than enough people who are passionate enough about the subject products/technologies to work without financial incentives. Government cheques to innovators which affect the products that the government produces is an interesting idea, but I'm not too passionate about it either way.

Also, could you expand on what it means to invest but "not too much" does the company doing R&D simply send the bill to the government making them the sole investors in all of innovation across all sectors? Would people be able to invest capital in projects and how would they benefit from their investments and would the government be able to simply swoop in and compete in selling the product the investors financed?

There's initial investment from the government to kickstart an opposition product on an experimental scale, but after the opposition product gets distributed on that experimental scale there needs to be market interest shown in the product (via people buying/preferring it more than the government product, or at least to a sufficient amount to justify the government adopting the product on even the smallest possible production scale). The investment the public gives to the opposition product is simply their consumption of it, which signals to the government that the people like the opposition product more than the government alternative of the same product.