> They want me to implement my knowledge in my new store to make a Customer Connection scores for go up.

There’s one thing I would caution, and just because I was in a similar position with you, just replace Customer Connection scores with Starbucks standards.

I made the mistake of not utilizing my shift team to help implement those things. While they were all on board, everything that my manager wanted fixed came through me. Which was not a good look. But eventually, I figured like, oh this shift cares about food so any food standards were missing, we can talk about them as a team and then find ways for them to be the one to introduce it to the rest of them team. It definitely worked 100% better than them being like, okay she’s nice by why does she keep trying to change everything we’re doing? By the time their shift came back, they were actually sad to see me go, so it was a real turn around.

So TL;DR, my advice would be to utilize your shift team when it comes to implementing new strategies. Share the burden, share the success.

I would continue to be friendly and outgoing. I would avoid making comments or suggestions along the lines of “well at my store, we did it this way...” I would take the first few days as an opportunity to casually observe your new coworkers before doing any real coaching (as long as standards are not violated). Having a lot of knowledge is an asset, but it might come off as holier than thou. I’m always mindful of that when I transfer, and i still fail sometimes lol. I’ve been with the company since 2007 and have transferred to a lot of stores in that time. You will get treated like an idiot (by customers and baristas) probably for a while because they assume you’re new.
“Can I show you a trick I’ve picked up?” is a nice way to start coaching someone you barely know. You get their permission and they’re more likely to see it as constructive rather than condescending.
You’re going to do great! Good luck on your new adventure.

Implementing change is really hard, so get the rest of your shift team on board and work on one change at a time. That may be greeting every customer who enters, getting a name for every order, having a prepared small talk question, or anything else you want to try so long as it's small, specific and store-wide. When you check in a barista, make sure to share that action item, then be consistent about coaching. Don't try to change anything else until the whole team is on board and consistently using your first change. If you're a data-driven kind of person, ask your SM to get you the CC score breakdown by daypart.