When a phrase has been entered but the space bar has not been pressed, the search needs to be initiated if the search textbox loses focus. To address this, I have implemented the HandleBlurAsync method. While I am able to add the chip values, the current SearchText is not being cleared after adding it to the chip set.

<MudChipField T="string" Values="@Values" ValuesChanged="@((value) => ChipValuesChangedAsync(value))"
              Value="@SearchText" ValueChanged="@((value) => SearchValueChangeAsync(value))"
              StyleChip="@(_disableRadius ? "border-radius: 0 !important" : null)" Delimiter="@_delimiter" FullWidth="true" Disabled="_disabled" ReadOnly="_readonly"
              ChipColor="_color" ChipVariant="_chipVariant" ChipSize="_chipSize" WrapChips="_wrapChips" MaxChips="_maxChips" ChipsMaxWidth="_chipsMaxWidth"
              Closeable="_closeable" Variant="_variant" Label="ChipField" OnBlur="@(async (value) =>await HandleBlurAsync(value))" />

@code {
    char _delimiter = ' ';    
    int _maxChips = 0;
    int _chipsMaxWidth = 80;
    Color _color = Color.Default;
    Variant _chipVariant = Variant.Filled;
    Variant _variant = Variant.Outlined;
    Size _chipSize = Size.Medium;
    bool _wrapChips = true;
    bool _disabled = false;
    bool _readonly = false;
    bool _disableRadius = false;
    bool _closeable = true;
    /// <summary>
    ///List Values of the chip control.
    /// </summary>
    [Parameter]
    public List<string> Values { get; set; } = [];

    /// <summary>
    ///Input string for search filtering.
    /// </summary>
    [Parameter]
    public string? SearchText { get; set; }

    protected override async Task OnInitializedAsync()
    {       
        await base.OnInitializedAsync();
    }

    private async Task SearchValueChangeAsync(string? value)
    {
        SearchText = value;
        await Task.Yield();
    }

    /// <summary>
    /// Event when the chip list changes.
    /// </summary>
    /// <param name="values">list value from the chipset.</param>
    /// <return>Task</return>
    private async Task ChipValuesChangedAsync(List<string> values)
    {
        Values = values.Select(v => v.Trim()).Where(v => !string.IsNullOrWhiteSpace(v)).Distinct().ToList();
        await Task.Yield();
    }

    private async Task HandleBlurAsync(FocusEventArgs e)
    {
        if (!string.IsNullOrWhiteSpace(SearchText))
        {

            Values.Add(SearchText);
            await ChipValuesChangedAsync(Values);
            SearchText = null;
            await SearchValueChangeAsync(null);
            StateHasChanged();
        }
    }
}