Does the current public stable build also offer all those dynamic backgrounds selection?

not exactly how It works

It takes 3dayd to uneroll.yes

But to.get a stable build you must wait till the current public release become public

You cannot get an old.update to.overwrute a newer update

You must wait till the next public release

Two things: Which map is "dynamic"? Is there time of day changing, is there any building destruction, is there any weather changing? Because I havent heard of it or anything "dynamic" about TF maps. Also, I believe all the current "genre'" FPS are casual.

you can set your own image

https://support.xbox.com/en-GB/help/account-profile/customize-xbox-home/change-xbox-one-background

Customised image

Note Customised images must be smaller than 3 MB, and the best size for backgrounds is 1920 x 1080.

1. Copy a JPG or PNG file that you want to use to a USB device, and then plug it into your Xbox.
   
2. On your Xbox, select Customised image. A dialogue box appears that shows the contents of your console and attached USB device.
   
3. Select the USB device, and then choose your image.
   

Screenshot

1. Select Screenshot, then choose the one you want.
   
2. Select More actions (…) > Background > Set background.
   

Dynamic background

Note Dynamic backgrounds are only available on Xbox Series X|S.

1. Select Dynamic background.
   
2. Select the background art you want.
   
3. Select Apply.
   

Note Some dynamic backgrounds are only available through promotions with special edition hardware (like the 20th Anniversary Special Edition controller). To see one of these special dynamic backgrounds in your list of options, make sure your special edition hardware is turned on and in use with your console when you set your background.

Remove customised background

If you want to remove your background, select Remove customised background.

Use Microsoft Edge to set customised backgrounds

You can also set a customised image as your background while using the Microsoft Edge app on an Xbox console. To do so, find any image you like within the Microsoft Edge app, move the browser pointer over that image, select the Menu button  and then Set as background.

At this time, dynamic backgrounds are only available on the Series S/X and can't be customized. If the video you saw was done on a One, then the person doing it is doing something that violates the terms of service.

If you are on a Series S/X, when you go to settings and change your background, there's a section for dynamic backgrounds.

The term "dynamic" will mean different things to different people.

Some maps are "dynamic" in the sense that other things beyond the combat are happening graphically. You'll see some buildings/towers falling in the background, you'll see ships coming flying in/out of the map, etc... However, from what I've seen - none of
these things actually change the landscape of the maps or affect the gameplay at all.