I'm not an English teacher but here's a way of trying to understand these.

would can have various forms, but as used here "would you like coffee?" is not asking if you liked in the past, it's rather if you want now (or in the future) in a slightly more polite form. Would is a conditional. "would you take the blue or the red pill?" It's giving you a choice.

Can/could ask more about intent and whether you're able to do something. "Can you do X?" (Or could you do X? Is the same but a bit more formal). Is asking if the person is capable and wants to do something. "Would you do something?" Gives the person the conditional of either doing something else or just not doing it. It's a question with an "or else ...".

Could is also the past form of Can. "I could have done it (in the past) but I did not do it" vs. I can do it (now or in the future).

Hope it gives you a starting point!

To give you a final example using various forms:

"You could have Googled this, but you wouldn't want to waste time scrolling to the useless AI results, which I perfectly understand; we can't spend all day reading AI generated text."