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I think it's up to you - I use a Sonicare toothbrush (which is excellent and highly recommended) - my teeth / mouth feel a lot cleaner with toothpaste, the foam helps with the sonic action of the brush, than without - maybe yours are different.
You might not notice any immediate difference between toothpaste/mouthwash or not, but I guarantee other people will. I don't believe you can just brush with water and expect the same result on cleanliness/breath.
Also, one of the few immediate benefits I've found to wearing a facemask recently is that I can smell when my breath is a bit "off" way before any other method like licking the back of your hand.