Life exists as a way to release trapped energy that simpler processes weren't able to. Look at us, releasing fission ennergy trapped in heavy atoms by supernovae.

Every living thing radiates black body radiation which is higher entropy than sunlight.

Thermodynamics says that you can't decrease entropy in a closed system. Whatever life does, however it does, like any process, will not decrease entropy - and generally, will increase it over time. That life seems to generate and maintain order locally only tells you that it shoves the entropy it produces somewhere else, out of sight (ultimately it becomes thermal radiation).

It's like with a heat pump: it does not generate cold, it merely transports heat against a gradient, and in doing so, adds more heat of its own. It may seem like it creates cold, but that's only because you're sitting in front of the cold end, while the hot end goes to ground or atmosphere - i.e. a thermal sink so large that your contribution to it is almost unmeasurable.

Life, like any other physical process, provides additional pathways to increase entropy. Otherwise that process wouldn't have a gradient to go through.