Do commercially available whitening toothpastes actually have an effect on whitening teeth?

I'm worried because my teeth seem to be turning yellow from drinking coffee every day.
Dental whitening procedures are too expensive, so I'm thinking of trying whitening toothpaste first.
I doubt whether the whitening toothpastes sold in supermarkets or online actually have visible effects.
Actually, I'm worried because there are stories of side effects like teeth becoming sensitive due to the surface being shaved down.
If you have any products you purchased with your own money that you found effective or products you would recommend, please share your advice.