How to thank someone on the team for helping you?

The level of thanks will vary based on the level of help: It would be very weird (and awkward/annoying) if you sent someone a box chocolates or something for every little thing they helped you with.

What I will say though is that you should always write a personalized medium-effort message minimum for everything instead of the very lazy "thanks" or "ty" DM (that is a low bar that you should never stoop too).

Let's say someone helped you figure out some build issue where you simply mis-followed the onboarding wiki and missed a step. Even though the help was just 2-5 minutes of their time, you can send something like: "Even though it was small, I've been stuck on this for 30+ minutes, so I really appreciate the help! You saved me from potentially hours more of going nowhere 🤣".

There's a good lesson about Deep Thanks in the question asking course as well: https://www.jointaro.com/lesson/UwFI0QisFWFRiOx30HiJ/asking-great-questions-part-23-deep-thanks/

Your thought around public thanks is good. It makes the thanks more meaningful and gives the helping engineer more points in performance review.