The JLPT is really vague about what is on each test. So there are many kanji, vocab, and grammar points that are both on the N3 and N4. These might show up more often on the N3 exam but they also show up rarely on the N4.
My advice really depends on your goal. It’s probably better to learn them all because you’ll probably want to do N3 in the future anyway. When Japanese people use kanji they don’t care about the JLPT level so you might need that kanji someday.
However, if you are really struggling with kanji already maybe wait to study these kanji until you know some of the more common ones first. You only need to get 50% right anyway so if one of these kanji does show up on the N4 test it’s not the end of the world.
In regards to Shinkanzen books, they go way overboard. Don’t get me wrong they’re great but their questions are often much harder than the JLPT so you are more prepared. I never looked at their N4 book but I imagine there’s a lot of N3 stuff in it.