When measuring runout, did you install all of the lug bolts? ( Use some washers / large nuts as spacers to prevent the bolts from bottoming out.)

If you are measuring with just a single rotor allen head attaching bolt, the rotor will be skewed. Hubs with 2 bolts would exhibit less runout but it will still be there.

Rotor runout is a minor cause of braking shake and probably more noticeable with light braking than heavy.

With fixed calipers, the pistons on either side will slide in / out and with sliding calipers the caliper will shuffle absorbing runout during braking. ( Rotor is moving left to right , pistons track this motion. ) Now that said, runout will knock the pistons back when the brakes are released causing low peddle because the pistons now have to travel farther to contact the rotor.

Thickness variation is the major cause of braking shake as there is nothing to absorb the variation. ( Pistons move in and out together. )

If the bearings were bad the runout would not be in the same place and would be observed by shaking the rotor. A rusty hub face would cause the issue you have. The hub could be refaced on a brake lathe but the radius where the hub face hits the hub center needs to be maintained. A sharp corner here could cause a stress riser leading to cracking in the long term.

And, just for completeness, rotors that have grooves in them won't cause vibration alone. Other than looking "bad" they have little affect on braking once the pads wear in.