Use URI suffix as parameter and ignore when resolving page

Question

I'm trying to change the output of pages depending on the URIs last section. This will be used to enable the user to change the page's presentation by changing the URL (e.g. /path/to/page/xml would show the page's content as XML).

The mode-selector should be ignored when Wordpress queries the page, so all three URIs should result in the same page content but add a query-parameter mode without doing a redirect (the parameter should be internal only, not visible to the user).

Example:

Unchanged Page: /path/to/page

Mode 1:         /path/to/page/mode1 => /path/to/page?mode=m1
Mode 2:         /path/to/page/mode2 => /path/to/page?mode=m2

When I add a rule to .htaccess, the parameter is added, but the page is not found (404). Wordpress seems to use the original URI, instead of the rewritten one.

I tried varients of the following rule, without success:

RewriteRule (.+)/mode1$ $1?mode=m1 [QSA]

What am I missing?

Answer 1

@Aboelabbas gave me the hint I needed. Although I don't really know what I did different, here is the working code for all three modes I need:

<?php
add_filter('query_vars', function ($query_vars) {
  $query_vars[] = 'mode';
  return $query_vars;
});

add_action('init', function () {
  add_rewrite_rule(
    '(.+)/buchung$', // Rule for URLs ending with "/buchung"
    'index.php?pagename=$matches[1]&mode=booking',
    'top'
  );

  add_rewrite_rule(
    '(.+/[^/]+)\.xml$', // Rule for URLs ending with "/anything.xml"
    'index.php?pagename=$matches[1]&mode=xml',
    'top'
  );

  add_rewrite_rule(
    '(.+/[^/]+)\.json$', // Rule for URLs ending with "/anything.json"
    'index.php?pagename=$matches[1]&mode=json',
    'top'
  );
});