If you go to the ps4 page you will see that the last post is there
Is it necessary to do something for the post to appear on the homepage or should it appear by default?
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You are most likely using browser caching ? Therefore new visitors would see the newly published post just fine, but because you've previously visited the page its cached and therefore your browser cache hasnt expired.
Generally its good practice to clear all caches upon publishing posts/pages and/or activating or deactivating a plugin.
You can also disable page caching for the front page :
performance - page cache - Don't cache front page