Move a taxonomy page field to a different region
You can approach this in UI, Twig or PHP:

UI

You can create a View (show Taxonomy Terms) with display "block" and add "Term ID" as Context Filter, see this example for Users: How to move the user account/Profile 2 information from the content region to a sidebar region

Twig

Install Twig Tweak and place the field in a twig template:

{{ drupal_field('field_name', 'taxonomy_term') }}


PHP

Prepare the taxonomy term entity in a preprocess hook, see print custom image field for taxonomy page (page--taxonomy.html.twig) template