I wrote a small js script that get the ids of the Mastodon posts that have been displayed on my screen and removes the ones that already appeared. Hence enabling to only see freesh posts.

remove_already_seen_mastodon_posts.js

var store_seen_posts_ids = function () {
  var alreadyseenpostsids = localStorage.getItem("alreadyseenpostsids")

  for (el of document.querySelectorAll(".status")) {
    alreadyseenpostsids += "," + el.dataset.id.toString()
  }
  
  localStorage.setItem("alreadyseenpostsids", alreadyseenpostsids)
}

var remove_already_seen_posts = function () {
  var alreadyseenpostsids = localStorage.getItem("alreadyseenpostsids").split(",")

  for (el of document.querySelectorAll("div.status")){
    if (alreadyseenpostsids.includes(el.dataset.id.toString())){
      el.remove()
    }
  }
}

store_seen_posts_ids()
remove_already_seen_posts()

Note that it breaks the Mastodon feed when scrolling down after executing: