I’m also on android 13, samsung smartphone. The play services version is 23.33.16. In the unknown tracker settings, it says last scanned 2 hours ago. What does it say in yours? Also, I had location and bluetooth enabled between that time. Have locked/unlocked my smartphone multiple times. I have yet to see that green dot. I guess it’s a bug with play services for your smartphone.
It is very likely Samsung has whitelisted Play Service from showing the green dot, my Pixel certainly does not, although it probably should and a bug might have the made the whitelist invalid.
Even if whitelisted. Play services will still show in scan history, enable ‘show system’ apps to see all. You also have nearby device scanning and nearby share features, which could affect it.