As the question states in the title. If it's Thunderbolt 4, will a new Gigabyte add-in Thunderbolt 5 card work on these new motherboards ?
well, strictly speaking, there is no X870E with TB4, there is only USB4 that is compatible with TB4/3, that runs at 40G speed max.
Meanwhile, despite the fact if the MB has TB header or not, TB5 requires 80G bandwideth, which means that you have to use at least PCI-E 4.0X4 slot to install it so that you can get TB5 speed. However, there is hardly any X870E can offer this unless you want your grahic card work at 8X speed