This behavior was a surprise for me too.
I need to paste HTML for the conversion, not plain text made of html markup.
I understand the workaround, to paste it in a tool understanding html and then copy another time from the latter.
But it would be very easy to have both clipboards, the plain text (made of html) as it is now, and the html type too (same content), so that it get the right behavior when pasting in html capable tools, and the same behavior as now for text only tools.
Everyone would be happy, and it’s an easy code to adjust.