When I'm next to a beacon and I put on the haste effect (1 and 2), they don't work, while the other effects work. I noticed that due to the haste effect, the animation of the pickaxe in the hand is faster (it hits more per second) but the blocks do not mine any faster. Also there is only the pickaxe to affect, on the other tools of the walking effect.
Sorry in advance, I used a translator.