You'll be exhausted of the style after 1 to go straight into 2. I'd just play 2.
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I don’t think it’s necessary to play them in order. If you’re itching to play Octopath 2, go for it. The games are very similar, so if you play them one after another it would probably start to feel repetitive.
Completely different stories.
There seems to be consesnsus that 2 improves over 1 in almost everyway, so you may find the experience going back to be a bit underwhelming, but otherwise there should be no issue.
I would suggest playing it for it's own sake, since I liked the game. Maybe try the demo, see if it hooks you. But don't feel obliged to play it just because you want to start the second game, you will not have a lesser experience.
I would also note that in general people tend to agree that the second game is an improvement in many ways over the first one, mechanically and in terms of storytelling. So maybe it is a safer bet to start with the second one if you are not sure, then you could always go back to the first one later if you become a fan.
Play 1 now, wait for a damn good sale for 2 so you have time to recharge