Vim syntax highlighting region is not correctly highlighted

I want to highlight special regions in a special extension .html.specialext, the regions are Lua code in some delimiter, here it's {{ and }}.

Detecting custom filetypes is trivial but here is my code in .vim/syntax/specialext.vim:

if exists("b:current_syntax")
    finish
endif

syn clear
set syntax=html
unlet b:current_syntax
syntax include @Lua syntax/lua.vim
syntax region srclua start="{{" end="}}" contains=@Lua

Here is what it does:

The HTML works, but the snippets are broken.

Here is the stock Vim Lua highlighting:

This is not due to spell checking as :set spell and set nospell have no effect