I have a workaround that appears to be working for me on version 12.0.2503.10378 - at least in the Form Preview, I haven't tested in an actual process.
Javascript for Layout Designer:

/*Option 1 - Manual List of Options:
Rather than using the "Append choices to lookup results"
option to manually add values to the dropdown,
we are using this Javascript. This ensures that the single
value loaded from the lookup is auto-selected.
This function runs when the field is changed by the lookup
and when the form is first loaded.*/
LFForm.onFieldChange(AddDepartmentsToDropdown, {variableName: "department"});
AddDepartmentsToDropdown();
function AddDepartmentsToDropdown() {
  const additionalValues = [
    "Human Resources",
    "Accounting",
    "Contact Center"
    ];
  LFForm.changeFieldOptions( {variableName: "department"}, additionalValues, "add" );
}

/*Option 2 - List of Options from Lookup:
Rather than using two lookups to populate
options in the dropdown (one for the single selected
value and one for the list of possible values).
We are using this Javascript. This ensures that the single
value loaded from the lookup is auto-selected.
This does require two fields, one for each lookup.
The departments_from_lookup field can be hidden from view.
This function runs when the fields are changed by the
lookups and when the form is first loaded.*/
LFForm.onFieldChange(AddDepartmentsToDropdown2, {variableName: "departments_from_lookup"});
LFForm.onFieldChange(AddDepartmentsToDropdown2, {variableName: "department2"});
AddDepartmentsToDropdown2();
function AddDepartmentsToDropdown2() {
  let fullList = LFForm.findFieldsByVariableName("departments_from_lookup")[0].options;
  LFForm.changeFieldOptions( {variableName: "department2"}, fullList, "add" );
}

Just to confirm — are you saying that after enabling "Append Choices to Lookup Results", the dropdown choices are not automatically selected, or that the lookup results don’t appear in the dropdown choices at all?

I could be mistaken or totally misunderstanding…  But I feel like to have the “Append Choices to Lookup Results” option continue to work properly, you really need to also have the “Assign Values to Choices” option turned on too.

It might be a bug that it doesn’t work well without the values enabled, but I feel like this is something I have encountered as well.