This is a common misunderstanding of the 2nd law of thermal dynamics. A key point that everyone seems to forget about is that entropy creating disorder happens in a _closed_ system. The Earth and its biosphere are not a closed system.
Discussion
The universe is.
I think it is illogical to think that the Earth is producing all of this increase in order (as you previously implied must happen). Do you believe that somewhere else in the universe everything is becoming disorderly at a higher rate to make up for all of the order being created on Earth? That doesn't seem logically consistent to me.
Perhaps I wasn't clear, Earth is _not_ a closed system. There is energy being pumped into Earth's biosphere from the Sun. But given enough time the sun will exhaust it's hydrogen, turn into a red giant engulfing the earth (maybe), eventually leading to our solar system trending to a low energy state. But that may very likely be interrupted when Andromeda and the Milky Way merge leading to a time of increased star formation (high energy state). Ultimately yes, the universe will trend toward a low energy state, in the very distant future (deep time) the universe will be nothing but slowly evaporating black holes each many billions of light-years away from each other.
BTW I dislike the term "disorder" in the context as it implies something more akin to chaos, which is not really the case. Some would say a universe with nothing but evenly separated atoms expanding away from each other (the real end state) sounds quite "orderly".
Entropy isn't just about energy. It actually is about order and yes, progression to chaos. Just because the sun supplies energy does not mean you get order. If you add energy to ice you get less and less order as the water melts and then evaporates. The two are not equivalent.
You're thinking about energy and entropy in the wrong context you could add energy to ice by removing the heat surrounding it, bus increasing the ice. You don't need to add energy to ice to get it to melt the heat will naturally dissipate.
Here's a great YouTube video that could explain it better than I could: https://youtu.be/DxL2HoqLbyA?si=yH1_vHCpQrhIbsON
For what it is worth, I appreciate your questions and comments. They help strengthen my own beliefs by having me defend them logically and really think them through completely and not just in a superficial manner.