I thought that the tweaks added by this mod allow the player to "overeat", but through gameplay, I noticed that my saturation and hunger values go up even without eating anything. As of writing, my saturation value is now 7 digits high and continues to increase.

This is a known interaction with some mods. You have a mod in your pack that is constantly adding saturation (possibly through applying the saturation potion effect). It's not a bug in the mod because normally food and sat are capped at 20 each, so constantly reapplying the effect will only reset it to 20. However, PiTweaks removes that cap, allowing it to go arbitrarily high. This isn't a bug in PiTweaks because vanilla MC doesn't let you eat food when your bar is full, so normally you are still somewhat limited by how powerful was the last thing you ate. The problem is that the combination is extremely unbalanced. I wrote the feature for my adventure server to stop wasting precious food when you eat near full hunger to heal.

If you run a PVP server, you probably want to turn off the playerUncapSaturation and playerUncapFood configs in pitweaks.toml.

If you have suggestions how to change it, please give them here. I thought about raising the cap instead of removing it. I'm not sure how high. I've seen modded foods that add 100 or more saturation. And as you've seen, there are some mods that will just hold you at max saturation no matter what the cap is, so it doesn't matter if it's 20 sat, 50 sat, or 10 million sat.

I already know what mod in my modpack causes this. Temporarily disabling the mod solves the issue.

To be specific, the mods that causes this interaction are mods that add autofeeders (which I have in my modpack). Disabling autofeeders on those mods solves the problem.