What are the things that lead to the speed or slowdown of the changes that I make on my site, when I use WordPress the changes appear quickly when I open the site on the browser, unlike when I make these changes using a program WYSIWYG
What program are you using, if not just the WordPress editor?
As soon as the change hits your database, the site should be updated. However, you need to keep caching in mind - your browser might hold on to old resources. Try opening your site in an incognito tab if this happens again. A CDN like Cloudflare (if you’re using one) could also be the culprit.