Radeon RX 6700 XT cannot start display manager / black screen

The recommended driver for the newer cards right now is the video-linux driver aka amdgpu.
Are you perhaps on an older kernel? Complete support for the newer cards has just arrived in 5.12, so that might be worth a try. Alternatively the 5.10 version had decent support for my 6800XT.
You might also need to check and change your Xorg config, to represent your new system and how everything is connected.