Htaccess www to non-www but keep the url intact - .htaccess

Question

I think that this is rather simple, but I just can't wrap my head around it.
I have a domain like https://www.example.com
I want to rewrite it to https://example.com
That works. But I am also rewriting other urls like https://www.example.com/privacy
If I try to rewrite these too the user is always redirected to https://example.com/privacy.php
How do I prevent my server to show the actual filename instead of its rewritten url?
My code looks like this:
RewriteEngine On
RewriteCond %{HTTP_HOST} ^www\. [NC,OR]
RewriteCond %{HTTPS} off
RewriteCond %{HTTP_HOST} ^(?:www\.)?(.+)$ [NC]
RewriteRule ^ https://%1%{REQUEST_URI} [R=301,L,NE]
RewriteRule ^checkout checkout.php [L]
RewriteRule ^imprint imprint.php [L]
RewriteRule ^privacy privacy.php [L]
RewriteRule ^terms terms.php [L]
RewriteRule ^allergy allergy.php [L]
RewriteRule ^nutrition nutrition.php [L]
RewriteRule ^order/([A-Z]*)?$ confirmation.php?lang=&id=$1 [L,QSA]
Any help is appreciated.
Regards

Answer 1

Have it this way:
Options -MultiViews
RewriteEngine On
RewriteCond %{HTTP_HOST} ^www\. [NC,OR]
RewriteCond %{HTTPS} off
RewriteCond %{HTTP_HOST} ^(?:www\.)?(.+)$ [NC]
RewriteRule ^ https://%1%{REQUEST_URI} [R=301,L,NE]
RewriteRule ^(checkout|imprint|privacy|terms|allergy|nutrition)/?$ $1.php [L]
RewriteRule ^order/([a-z]+)/?$ confirmation.php?lang=&id=$1 [L,QSA,NC]
Make sure to test after clearing your browser cache. Problem appears to be due to your patterns not using end anchor.
I have combined your multiple similar rules into one rule.