Computing is a task. Printing is a task. It’s not wrong to call both a human and a machine a “computer”, because computing (applying an algorithm to an input and producing an output) is literally what they are doing. Same way you can have human and machine diggers, cleaners, calculators and lots more.
Anthropomorphizing comes in when we attribute much more complex behaviors to them - chain of thought, reasoning, intelligence. At that point you aren't talking about mechanical concepts but claiming that these machines are exhibiting human behavior.
Whenever we reason, we are not neurotically bruteforcing the possibilities (although sometimes we do, like proof by exhaustion), usually we make predictions heuristically of which assumptions or theorems apply or might apply. It's not any different for machine proof assistants...
I think a problem is that previously thought, reasoning, and intelligence were always co-occurring, but now we have machines capable of (limited) reasoning that do not think or have intelligence.
Anthropomorphizing comes in when we attribute much more complex behaviors to them - chain of thought, reasoning, intelligence. At that point you aren't talking about mechanical concepts but claiming that these machines are exhibiting human behavior.