In the dictionary, they say
to put or fasten bricks, a carpet etc in the correct place, especially on the ground or floor
The carpet was laid last week.
The project involved laying an oil pipeline across the desert.
It seems that when we say "The construction worker laid tiles", the part "on the foundation" or "on the floor" is implied.
But, if you have to make it clear, then
Is it technically correct to say "The construction worker laid tiles/carpets/ wood on the foundation(s) of the house" or "The construction worker laid tiles/carpets/ wood on the floor of the house"?
Does "floor" mean it has already had a layer of carpet or wood or tiles on it?
Also, the noun "foundation" is countable.
Is there just 1 foundation in a house or many foundations in a house? For example, each room has a foundation or what?