See https://en.wikipedia.org/w/index.php?title=User:JohnCD/VEtest&diff=prev&oldid=561397375 - the header is de-headered, and a spurious nowiki tag added.
This link is dead, it seems the page was deleted.
I can't reproduce this. I'm not sure what the original issue was, given the missing reproduction page, but a heading at the beginning doesn't seem to behave in any way differently than other headings.
To copy a heading along with the formatting, you have to select it together with the closing tag, which is a bit awkward and not obvious, but it's the same for all headings.
I peeked at the revision:
==L2 Header== ===L3 header=== Some text including '''bold '''and ''italic ''and '''''both '''''at once [..] ==Fourth L2 header==
==L2 Header== ===L3 header=== Some text including '''bold '''and ''italic ''and '''''both '''''at once [..] ==Fourth L2 header== L2 Header ===L3 header=== Some text including '''bold '''and ''italic ''and '''''both ''at once ===Another L3 header=== This line includes a [[Wikipedia:Wikilinks|wikilink]] as a sample ==<nowiki/>==
I presume the edit was to select from start ("L2 Header") until end of first sentence, copy that, and paste at the end. Nothing the bugs: 1) L2 Header didn't become a heading, and 2) odd <nowiki/> in a heading at the end. I could not reproduce this on testwiki today. Closing as resolved.