I haven't smoked in 1 week, then I only did a few puffs.

Well, although people have different approaches to this, my feeling is that if you are counting days, and that count is "number of days since I last smoked" then yes, you need to reset. Honesty, with yourself especially, is really important in this.

Your habit will find any crack to get you smoking again, and if you're not honest with yourself it will exploit that weakness.

That said, as a wise person on this sub once said, "So you've had a lapse, now it's up to you to decide whether it will be a relapse."

So my take is that you reset your day count, learn from your mistake so you can avoid hitting it again, and get back on track.

Well you didn't binge so not at all. As for what day you're on... That's your choice. I did similar and didn't reset my day back to 0 til I felt it wouldn't affect me. As in, I got to I think the point where I slipped before I said "sod it, it's not day 14, it's day 7, I can change to counter to when I last had weed." Just don't let the slip demoralise you. That's what's most important

Only you can decide that, everyone has different perspectives. If you don’t smoke again afterwards then this will be the tiniest blip in the rest-of-your-life sobriety so what does it matter? If you let it be more than that then it is more than that!