Field Parameter with value from column

Yes, this is possible, but not with a single field-parameter slicer.

To achieve this behavior, you need two disconnected slicer tables and a filtering measure.

First, create a small table to choose what you want to filter by (App Owner or Group):

Dimension Selector table
App Owner
Group

Next, create another table that holds all possible values for both App Owner and Group:

Value Selector table
Person A – App Owner
Person B – App Owner
Person C – App Owner
Data – Group
Dev – Group

Then create a measure to apply the filter based on the selections:

Dynamic Filter =
VAR SelectedDimension = SELECTEDVALUE(DimensionSelector[Dimension])
VAR SelectedValue = SELECTEDVALUE(Value Selector[Value])
RETURN
IF (
SelectedDimension = "App Owner"
&& ( ISBLANK(SelectedValue)
|| SELECTEDVALUE('Table'[App Owner]) = SelectedValue ), 1,
IF ( SelectedDimension = "Group"
&& ( ISBLANK(SelectedValue)
|| SELECTEDVALUE('Table'[Group]) = SelectedValue ),1,0))

Use the model like this:
Slicer 1 → Dimension Selector[Dimension]
Slicer 2 → Value Selector[Value]
Apply the Dynamic Filter measure to the visual and set it to 1.

Result:
If App Owner is selected with no value, all persons are shown.
If App Owner and Person A are selected, only Person A is shown.
If Group is selected with no value, all groups are shown.
If Group and Data are selected, only Data is shown.

This approach works reliably and avoids limitations of field parameters.