Аutomatically clears the cache whenever a new post or page is created?

in this case, the preload feature creates cache before visitors. you can publish a new post when you have a low traffic. and you can speed up the preload feature as below.
https://www.wpfastestcache.com/features/manually-preload-with-cron-jobs/

Thanks!

Do I understand correctly that your plugin works like this:
1) I publish a new post.
2) Someone goes to the page with this post (for example, myself) and at this point the server creates a cache, which will be available to other users.

Question. When I publish a new post, my homepage and the post archive (category) page will automatically refresh. Will the user accessing these pages see the old cache or … publishing a new post will start the process of updating these pages too?

1) I publish a new post.
2) Someone goes to the page with this post (for example, myself) and at this point the server creates a cache, which will be available to other users.

yes.

(category) page will automatically refresh. Will the user accessing these pages see the old cache or … publishing a new post will start the process of updating these pages too?

The user does not see the old cache. The user see the changes exactly.

Thank you! That sounds wonderful. With other caching plugins, we have encountered exactly the situation that users have seen old posts. Do I understand correctly that this feature is in the free version? I will try out your plugin and I have already read what features the paid version has. If everything will work as it should, then it is a must-have on the site.

this feature exits in the free version.