if form alter we can do it using 2 methods
using form object or using form state object and loading data from node
function custom_module_form_alter(&$form, FormStateInterface $form_state, $form_id) {
if($form_id == 'node_page_edit_form'){
$tid = $form_state->getformObject()->getEntity()->get('field_term')->getValue()[0]['target_id'];
dpm($tid);
}
}
Below is example for getting term from Form objects fields default value
function custom_module_form_alter(&$form, FormStateInterface $form_state, $form_id) {
if($form_id == 'node_page_edit_form'){
$tid = $form['field_term']['widget'][0]['target_id']['#default_value']->get('tid')[0]->getValue()['value'];
dpm($tid);
}
}