When working with the attribute forms value map or value relation i have found no way to switch between raw field values and displayed values in the attribute table (neither in the project properties nor in the program options). Is there any?
Not that I know of. The only way I know of is to change the edit widget type from value map to the default widget for that data type, eg range for numerical fields. That's not a good solution because you'll lose your value map settings. You can save different widget types as separate layer styles, and switch between them, but that's a bit cumbersome.
As a workaround, create a virtual field to display the raw field values.
For example, I have a numerical field "color" with a value-map widget. The user selects a color from the dropdown menu, and the corresponding numerical value is stored in the field. However, in the attribute table you can only see the text name of the color.
So I add a virtual field called "color_code" with the expression
This field displays the raw value from the color field.
Note: when I change the "color" value in the attribute table, the attribute table doesn't display the updated "color_code" value unless I close the table and re-open it. This is a long-standing bug in QGIS.
You can also see the raw value for each feature labeling features with the value-mapped field.