'Search your deck' abilities do not search the deck.

ChurchPews

Searching the deck is a quick way in the real game to be able to see what's prized. In TCG live however, it will not show you the entire contents of the deck.

While I appreciate having quick access to the relevant cards for the function, this makes some niche decks near impossible to use properly as knowing what's in your prize pool is crucial.

Flagrama

In the top left corner you can switch between valid choices and your whole deck.

ChurchPews

Ah sick, I've never noticed somehow and have looked for it.

I will say in this case then it's certainly not in an intuitive position