Thanks for including the video that helps us out a bunch with these kind of issues. The pulley on top looks like its loose and shaking. might need adjusting might need to be replaced can't say for sure. Try to move it when the car is off and see how much play there is in it before you take the belt off

new info: the damper pulley had a broken screw inside; the tensioner feel okay when i turn it by hand -a decent force was needed to turn-

since the water pump is driven by the timing belt, ill run the engine without the drive belt to pinpoint the vibration. ill remove the tensioner to see if there is damage.

ps: correct me if its a bad idea

Hello.

Have you checked the Crankshaft Pulley,

It's made of rubber and prone to failure.

All the Best.

tensioner replaced, same movement, same vibration of the entire car

i discovered the cause of vibrations, was not the tensioner, damage front axle. prior to the problem, i replaced the c.v. joints and the rubbers in a local shop. they did not know how to install the c.v. joints properlly, hammering them to death damaging all the tooths inside the axle.
the cost of fixing it its making me think in junk the entire car.
lesson learned, ill never trust another mechanic again, ill invest in tools and fix all the issues by myself in the future. im really mad....a simple task that went wrong.

Yep me to i very rarley used machanics if i can do it my self i will iv done every yhing you can think of even engine rebuilds but never gearboxes that a specialist job most people now days are not even qualified to do the job internet certificates garage monkeys lol