I managed to fix the sitemap issue by creating a PHP page which lists all pages on the site and adding that URL as an additional starting URL in the sitemap generator settings. I have also added a pink to the HTML sitemap generated from the frontend so that search engines (if they also have the same issue as the sitemap generator) will now find the links that could not be accessed via pagination.
My question is: Would these interventions be sufficient to ensure all pages are crawlable. Is it a must or recommended to alter the pagination system as it currently fits in well with the new design?
Looking forward to reading your thoughts.