How can I print user field values in page.html.twig?
To print user fields on the page template create a Views block and place it in an existing region.

At best you first added a new view mode for User under https://example.com/admin/structure/display-modes/view and then on https://example.com/admin/config/people/accounts/display select the newly created view mode and place the fields you like to display.

Then create the view, have it display Users and in the very right under ADVANCED add a contextual filter for User ID. Select Provide default value and choose User ID from logged in user, save. Then in the very left under FORMAT > Show > User select the view mode you created earlier.



Don't print user values on the page template.


page.html.twig is for printing regions.
page.html.twig is cached per user role. Next user with the same role will get displayed initially cached values of another user.
The user object with all field values isn't fully loaded by default, you would need to preprocess the user first.
Templating should be done when you need to structurally change markup.