Thankfully, the answer to this question is a resounding no!
As was the case with Xenoblade Chronicles, Xenoblade Chronicles 2 and Xenoblade Chronicles X, this latest addition tells an almost entirely separate story that's set in a brand-new world with an all-new cast of characters. Yes, there's some clever continuity here as the events that transpire in Xenoblade Chronicles 3 follow on in some cool ways from those in its predecessors, and there are some nice surprises along the way for those of us who've lapped up every second of this stellar series so far, but none of this will hold you back or create any sort of barrier to understanding everything that takes place this time around.
Further to this, Xenoblade Chronicles 3 does a great job of filling you in on the most important events leading up to the story that unfolds throughout its campaign with plenty of time taken to recall important aspects of previous games, meaning that every time there's something from an older entry that you really should know, it'll be referred to and shown to you here in cutscenes and/or through conversations.
Of course, as huge fans of this franchise, we wholeheartedly recommend that you take the time out to play all of the previous titles, but that's a very big undertaking, these are seriously meaty games and, if you're understandably finding yourself caught up in all the hype and just want to get started on part 3 at the same time as everyone else, rest assured you'll be able to follow the story, get stuck into the combat and enjoy every big emotional moment without having to do your research first. Aionios awaits!