Calling all turners: question on acceptable degree of runout

I turn a little but I am by no means an accomplished Turner. I buy way more sandpaper than a Turner does. .

It’s hard to tell without using a micrometer to check headstock runout, but it doesn’t look like the headstock is the issue from your little video. I don’t see the same runout apparent there. If @YrHenSaer ‘s suggestions are sound and obvious.
Morse taper connections need to be spotless to work properly. Even old packing grease that wasn’t cleaned out of the taper can introduce error. A bottle brush and some mineral spirits will clean out the headstock taper.

Is that a MT1 to MT2 adapter in the middle? If so, get rid of it and get a proper MT2 drive center. You are compounding the chance for error.
You should be able to get within .001” or ..002” (.025 to .05 mm ) without much trouble with a proper setup.. That won’t be noticeable.
I suppose its possible the headstock shaft or bearings are bad, but I’d try the other things first.

But part of your your question was whether it would affect bowl turning. With proper steps, it won’t unless it isn’t runout but a worn out shaft or bearings .( not likely if you bought the lathe new) You will be able to rattle the headstock by hand in that case. Some lathes have adjustments that allow you to preload the bearings to eliminate slop. Check your owner’s manual.
Keep in mind that if you are thinking of bowl turning, you won’t be using the drive center, but rather a faceplate or a chuck. A faceplate,will be better if you do have issues with concenticity.
You can cancel out any errors with a faceplate that has a sacrificial wooden plate on it. You true up the wooden bit before you attach your bowl stock to it.

True up the edge , then the face of the sacrificial wooden faceplate with a stiff sanding block on the lathe and then either glue using the paper trick or screw your bowl blank to the trued up piece.