That 500 error page usually indicates a problem with your .htaccess file.
Looking more closely at your .htaccess setup, I think I can see why that is.
My recommendation for setting up Laravel is to put a small .htaccess file in the htdocs directory and leave the official htdocs in-tact.
You appear to have moved the original .htaccess and have attempted to modify it for the different subdirectory. It’s possible to make a Laravel site work that way too, but it’s a lot more complicated and more likely to break with upgrades. Your current rules are not cutting it, at least.