My experience with the official dock has been quite negative, it would sometimes not work until the power cable is unplugged and then plugged back - that is with all the latest stable updates for everything. Other people on Steam forums run into this issue too.

https://steamcommunity.com/app/1675200/discussions/3/3472864793317268180/

https://www.reddit.com/r/SteamDeck/comments/y3wbad/i_have_to_unplug_dock_every_time_i_change_inputs/

https://www.reddit.com/r/SteamDeck/comments/137tiut/steam_deck_dock_requires_unpluggingreplugging/

https://www.reddit.com/r/SteamDeck/comments/y59bl9/no_signal_when_i_connect_steam_deck_to_tv_using/

I’ve noticed the issue too late for a simple refund process and their support was not cooperative at all.

I recommend looking at other docks instead, will cost you less and work better.