Here's one solution :
1- Attach a script to your TextureRect.
2- Connect your CenterContainer's "resized()" signal to your TextureRect
(Click on your CenterContainer and check the "Node" panel)
3- Then on your newly created function, add :
rect_min_size = get_parent().rect_min_size * 0.8
Your function name may differ if you named your CenterContainer otherwise
4- On your TextureRect, Check the "expand" box just below the texture.
Then as you change your CenterContainer's min_size (or size, you'll have to adapt a bit), your TextureRect should adapt