I solved my problem with the following approach:
In the field which holds the boolean value, I defined a checkbox as edit widget under layer properties -> fieöds and set the representation for checked as t and for unchecked as f ( see image) [![enter image description here][1]][1]
Another but similar approach is to use a value map field and use the two options (image 2)
[![enter image description here][2]][2]
I then defined a standard layer style for my layer in QGIS and saved this style into the database with properties -> style(the button down left) -> Save as default -> Save to datasource database
So every time I load the layer the bool field is shown as checkbox which is either t or f and which is understood by Postgres as a boolean value and if I query the field inside postgres with:
SELECT bool_field from my_table
I get something like
bool_field: false, false. true, ... [1]: https://i.sstatic.net/GZlmy.png [2]: https://i.sstatic.net/h6SLw.png