.htaccess case-insensitive directories - regex

Question

I access to the file.php writing mydomain.com/file. I need to be able to access also writing mydomain.com/FILE.
In .htaccess I use the following rules to remove extension:
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)/$ /$1 [L,R=301]
RewriteCond %{DOCUMENT_ROOT}/$1.php -f
RewriteRule ^(.+?)/?$ /$1.php [L]
# redirect to .php-less link if requested directly
RewriteCond %{THE_REQUEST} ^[A-Z]+\s.+\.php\sHTTP/.+
RewriteRule ^(.+)\.php $1 [R=301,L]
If this rules should be changed- it's up to you.

Answer 1

Define this RewriteMap in Apache or vhost config:
RewriteMap lc int:tolower
Then inside your .htaccess have an additional rule to lowercase all uppercase URIs:
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)/$ /$1 [L,R=301,NE]
# redirect to .php-less link if requested directly
RewriteCond %{THE_REQUEST} ^[A-Z]+\s.+\.php\sHTTP [NC]
RewriteRule ^(.+)\.php$ /$1 [R=301,L,NC,NE]
# convert each REQUEST_URI to lowercase
RewriteRule ^(.*?[A-Z]+.*)$ /${lc:$1} [R=301,L,NE]
# internally add .php
RewriteCond %{DOCUMENT_ROOT}/$1.php -f
RewriteRule ^(.+?)/?$ $1.php [L]

Answer 2

Use [NC] flag in your rules
Use of the [NC] flag causes the RewriteRule to be matched in a
case-insensitive manner. That is, it doesn't care whether letters
appear as upper-case or lower-case in the matched URI.
https://httpd.apache.org/docs/current/rewrite/flags.html

Answer 3

You need to take care of two aspects: first the case insensitive matching and second the case conversion to lowercase.
Apache's rewriting module provides the NC flag for the first aspect and a somewhat more complex approach to the second one:
RewriteEngine On
# remove trailing slash (/) if no such folder exists
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)/$ /${lc:$1} [NC,L,R=301]
# internally rewrite to a php script if it exists and convert to lower case
RewriteCond %{REQUEST_FILENAME}.php -f
RewriteRule ^(.+)$ /${lc:$1}.php [NC,L]
# redirect to .php-less link if requested directly
RewriteRule ^(.+)\.php$ ${lc:$1} [NC,L,R=301]
I have the impression though that your original set of rewriting rules does not really achieve what you attempt to, that is it syntactically invalid even. That is why I changed a few aspects.