When will my samsung galaxy A71 5G get upgraded to Android 13?

unsure. its completed per their site for TMO however not to sure how long ago it was completed and or when they’ll start kicking it out.

https://www.t-mobile.com/support/support/phones-tablets-devices/software-updates

You have gotten ghe update last week  or so. 

But you can check out the site  below and you can get more information there. Also, this will be the last  update for the A71 5G. 

https://www.sammobile.com/news/samsung-devices-eligible-for-upcoming-android-13-update/

Or just log into your samsung account  and  get all the information you need .