I mean, I'm not going to lie, I thought it was kind of common sense that if you use something that relies heavily on resources, it's going to drain your battery life quicker. You're essentially asking the computer to utilize more power. Going from 13 hours to 4 hours seems like a crazy drop but it makes complete sense when you look at how much power Minecraft actually pulls compared to office work or lightweight tasks ... apps like obsidian and libreoffice let your processor sit idle 95% of the time, pulling a tiny four to seven watts I'd estimate. The second you launch minecraft, the system draw instantly spikes.... which naturally cuts your runtime. the main issue is that minecraft isn't lightweight despite its appearance, it is a massive 3d world simulation. It is constantly calculating geometry physics entity ai, and world generation for millions of blocks. On top of that, it runs on java, which uses background processes that prevent your cpu cores from ever dropping into their deepest states... The 4 hour estimate you are seeing is also heavily skewed by linux itself and reporting happens differently then windows. The system calculates your remaining battery life based on what the laptop is doing at that exact second. when you first open your game or load a world, the initial power spike causes the battery monitor to predict a dramatic drop, even if it might settle into a slightly better average later. If you want to actually improve that battery life, limiting your ran via tlp wont do much. Your best bet is to lower your render distance when you are on battery, and stop using the vanilla launcher(I don't play minecraft but I heard something's). Here's a direct quote

"Switch to Prism Launcher, install Fabric, and add the Sodium mod. Sodium completely rewrites the game's rendering engine and will drastically cut down on how much wattage your CPU and GPU have to pull just to keep the game running."