how to print value of a taxonomy field to headline with node.html.twig?
That's because a taxonomy field has no values. It contains entities, which are the referenced terms. You get the first term with .entity and then you can get the values inside of the term, for example if the term would have a field_test2:
{{ node.field_test1.entity.field_test2.value }}

Or simply the term label (no .value needed for this):
{{ node.field_test1.entity.label }}

If you need translation use the |translation filter of the module Twig Tweak.