You aren't actually having a PHP problem.

The HTTP 405 error is being caused by your web server (Apache, Nginx, VS Code's static server, etc.), which is rejecting your POST request because it isn't set up to accept it.

HTTP 405 = "Method Not Allowed": The server is only permitting GET requests, but your browser is sending a POST.

You're serving pages via file:// or the built-in web server in Visual Studio Code, neither of which support POST.
POST requests to that endpoint are blocked by your real HTTP server.
The PHP code isn't yours. Your server is preventing POST.
Use the appropriate server: PHP -S localhost:8000 or an Apache/Nginx configuration.
Sort your files into distinct folders, such as send_email.php and index.html.
Diagnostics: Verify that POST is permitted by looking through error logs and server configurations.