There is a distinction between data and an action you perform on data (matrix maths, codec algorithm, etc.). It’s literally completely different.

Incorrect. You might want to take an information theory class before speaking on subjects like this.

I literally cannot be wrong that LLMs cannot think or reason, there’s no room for debate, it’s settled long ago.

Lmao yup totally, it's not like this type of research currently gets huge funding at universities and institutions or anything like that 😂 it's a dead research field because it's already "settled". (You're wrong 🤭)

LLMs are just tools not sentient or verging on sentient

Correct. No one claimed they are "sentient" (you actually mean "sapient", not "sentient", but it's fine because people commonly mix these terms up. Sentience is about the physical senses. If you can respond to stimuli from your environment, you're sentient, if you can "I think, therefore I am", you're sapient). And no, LLMs are not sapient either, and sapience has nothing to do with neural networks' ability to mathematically reasoning or logic, you're just moving the goalpost)