With Clean Pasting set to "Basic", when pasting an HTML H1 or H2 tag into a Header block, in the resulting email the style is not applied to the header (because the pasted H1 tag is placed outside of the header H tag).
See video demonstrating the problem: https://share.getcloudapp.com/5zuOvJ0q
Here is a link to the JSON template that is produced: https://share.getcloudapp.com/P8uXwRxW
As a fix, I'd suggest stripping H1, H2, H3, H4 tags when clean pasting is set to basic.