mod_rewrite trouble with /product/?id={xyz} to /product/{xyz} - .htaccess

Question

My attempt:
RewriteCond %{QUERY_STRING} ^id=(.*)$ [NC]
RewriteRule ^/product$ /product/%1 [NC,L,R=301]
I want to apply this rule to /product/ and /supplier/ directories only. They are both first level sub directories.
Note: product/?id={xxx} is actually product/index.php?id={xxx}. Apache hides my extensions and indexes. Just want to point that out.
My product/index.php handles the parameter given and determines what page it should show:
index.php
if ( isset( $_GET['id'] ) && !empty( $_GET['id'] ) ) {
//html for individual page e.g. /product/?id=foo
//e.g. <h1><?= $_GET['id'] ?> Page</h1>
} else {
//html for product list e.g. /product/ (no parameters)
}

Answer 1

Try this in one .htaccess file at root directory:
Options +FollowSymlinks -MultiViews
RewriteEngine On
RewriteBase /
RewriteCond %{QUERY_STRING} id=(.+) [NC]
RewriteRule ^(product|supplier)/?$ /$1/%1? [NC,L,R=301]
In .htaccess files the URI-path test it in the rule does not have a leading slash (^/product), therefore the regex cannot have it either. The trailng ? deletes the incoming query.
If the rule-set is to be placed at Apache main configuration files, the leading slash should be kept: ^/(product|supplier)/?$
UPDATE
To show the wanted URL but still get the data from the original URL.
Request: /product/?id=parameter
Options +FollowSymlinks -MultiViews
RewriteEngine On
RewriteBase /
RewriteCond %{THE_REQUEST} ^(GET|HEAD)\s/(product|supplier)/\?id=([^\s]+) [NC]
# Strip the query and redirect permanently
RewriteRule ^(product|supplier) /$1/%3? [R=301,L,NC]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{QUERY_STRING} ^$
# Map internally to the original request
RewriteRule ^(product|supplier)/([^/]+)/? /$1/?id=$2 [L,NC]
Another option is to use directly the "pretty" URL in the request:
Request /product/parameter to /product/?id=parameter
Options +FollowSymlinks -MultiViews
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{QUERY_STRING} ^$
RewriteRule ^(product|supplier)/([^/]+)/? /$1/?id=$2 [L,NC]