Can not set text field format to a field with multiple items

I am unsure this is a bug. Show your code implementation.

Code:

// Set the abstracts array
foreach($abstracts['abstract'] as $key => $abstract){
$abs_items [] = '

Insight ' . $ins_items[$key] . '

' . $abstract;
}
// Set the field
$Node->set('field_design_abstract',$abs_items);
$Node->save();

Did you try?:

foreach($abstracts['abstract'] as $key => $abstract){
       $abs_items [] = [
            'value' => '<p class="ins_t">Insight ' . $ins_items[$key] . '</p>' . $abstract,
            'format => 'full_html',
       ];
}
// Set the field
$Node->set('field_design_abstract',$abs_items);
$Node->save();

Your #4 works fine, thanks.
However...2 questions:
1. Why do you need to set the format explicitly as the field itself already defines the allowed format
2.  I used the following which did not work..
$Node->field_design_abstract = $abs_items;
$Node->field_design_abstract->format = 'full_html';

I’m glad I could help. You should examine the field values programmatically to see why this is the correct way.