Hello
It depends on how it is formulated in your building permit.
The house construction itself is irrelevant for the archaeologist. It is purely about the soil, i.e. the earthworks.
The archaeologist stands next to the excavator during the topsoil removal and watches to see if any findings emerge. It is already clear whether "digging" is necessary or not. If the topsoil removal is inconspicuous on ALL relevant (!) areas (including the wall), they fill out a form (which you and the monument authority receive) and then you can start building and will probably never be bothered again.
If findings come to light, it depends on the construction depth:
1. construction depth was reached: covering with geotextile basically suffices....(consultation with the monument office - but this is done by the archaeologist)
2. construction depth was not reached: excavation until reaching the construction depth, possibly a complete excavation, depending on the find/situation...
I don't know which state you live in. In Bavaria, different companies can be commissioned for the topsoil removal and the actual excavation:
the topsoil removal is one measure and the excavation itself is another measure. Therefore, they can be awarded differently....(but it doesn't really make sense)