I do like @StrangeTech 
And I remember having troubles as well overiding templates at some time, and I found thid in WP dev docs:
You can clearly see here that your blog page will never use the archive.php template, but only home.php or index.php. Blog index page is not considered as an archive by WP.
And when I tried, I couldn’t overide this, even with Cwicly conditions. Index template seems to be forced on blog page.
What I find strange is that it seems we can’t create the home.php template in FSE (or Cwicly), so using the index.php template seems the way to go.
Check this thread: