Does anyone know why Destiny 2 on Xbox's profile game history has been renamed to Destiny 2...

Your best bet would have been to purchase The Destiny 2 Forsaken complete collection, yeah it comes with Destiny 2 full game, but comes with all dlc too, and the price has been knocked down by 60%. Here is the link

https://www.microsoft.com/p/destiny-2-forsaken-complete-collection/bpdf10q2wh07

Destiny 2 has a confusing amount of choices in the Microsoft Store, are you absolutely sure you purchased the correct package? According to this URL, the Destiny 2 Digital Deluxe Edition appears to include everything available so you should be able to play
the new content:

https://www.microsoft.com/en-ca/p/destiny-2-forsaken-digital-deluxe-edition

Log into your Microsoft Account and double check your purchase history to confirm that you purchased the correct Destiny 2 package.

I would say Destiny 2 has been my best game of this gen

destiny 2 seasons are but the actual dlc is not and never has been.

I’m not playing on console. My mates are. And I’m using the Xbox game bar on pc to party up with them while playing destiny 2 on pc, destiny 2 has cross play so I use the game bar to party up with Xbox console players. Also I have a Xbox series s if i do the steps above does the console need to be on or no