Will my Warzone game progress be lost if I later get the entire Cod modern Warfare game on disk?

I have been playing the free battle royal Modus Warzone on my Xbox one for a few months now and therefore I have quite a lot of progress. Now I want to buy the whole game to get access to the other online modes and the campaign and, because it is cheaper to buy the game as a disk than if you buy it online, I wanted to do that too. My question is now:

will my progress and my scores be lost as a result and I will have to re-acquire all skins, weapons, sprays etc. Or is this secured via my activision account and I can then continue playing directly at the current status?
My other question would be about space. The game is currently consuming around 110 GB even though it is only warzone. What would it look like if I got it on the disc? Would I have to download all of this again and will it become more or will it remain the same?

LG and thanks in advance for every answer

Everything is saved on your activision account, the game also has cross play so you could buy the game on any other device and keep your progress