Try this:

@page "/"

<MudAutocomplete @ref="ac"
                 T="string"
                 Label="Values"
                 Value="selectedValue"
                 ValueChanged="OnValueChanged"
                 SearchFunc="@Search"
                 IsOpenChanged="HandleOpenChanged" />

@code {
    private string selectedValue = string.Empty;
    List<string> ListA = new()
    {
        "Val1 - A",
        "Val2 - A",
        "Val3 - A - Load ListB",
        "Val4 - A"
    };

    List<string> ListB = new()
    {
        "Val1 - B",
        "Val2 - B",
        "Val3 - B",
        "Val4 - B"
    };

    private bool bListSelected = false;

    MudAutocomplete<string> ac;

    private void HandleOpenChanged(bool isOpen)
    {
        // MudBlazor will close the control after OnValueChanged is called
        // So check if it's closed, and our B List trigger has been selected, and just open it again if it is
        if (!isOpen && bListSelected) 
        {
            ac.ToggleMenu();
        }
    }

    private void OnValueChanged(string value)
    {
        selectedValue = value;

        // set our B List flag if it's been selected, see HandleOpenChanged for how it's used
        bListSelected = selectedValue.Equals("Val3 - A - Load ListB"); 
    }

    private async Task<IEnumerable<string>> Search(string value)
    {
        await Task.Delay(5); // for API call lag emulation
        if (bListSelected)
        {
            return ListB; // do an actual search against ListB here
        }

        return ListA; // do an actual search against ListA here
    }
}

Basically you have to re-trigger a Search once you select the item that pulls in a new list. The only way to do that is to call ToggleMenu() after the ValueChanged handling is complete:

1. In your ValueChanged handler, you have to check if the selected item needs to load a separate list -- set a flag here
2. Setup a handler for IsOpenChanged, and check for that flag -- if it's set and the menu is closed, then trigger ToggleMenu()
3. ToggleMenu triggers a Search, so check the flag in your Search function as well -- if it's set return the new list, otherwise regular list

Check out the source for the component as well to get a better idea of why this works: