Inlinetasks are always interpreted to be of type heading. This causes multiple issues e.g with export.
I think that I could track it to the function org-element--current-element, where the check for headings is before the one for inlinetasks, while inlinetask is just a sub-type of heading.
Hence the (custom-) formatting of inlinetasks at export does not work.
Org mode version 9.5 (9.5-gced2b3