I think you've left out the code for your drop target, as most of your CSS styles aren't referenced.

However, it appears that your drop target is positioned on top of your files list. Note the z-index in your CSS...

.drag-drop-input {
    position: absolute;
    width: 100%;
    height: 90%;
    opacity: 0;
    cursor: pointer;
    z-index: 2; /* <== here */
}

This would create a glass-pane type effect. You can see your files list and remove buttons, because you have opacity: 0; - however you can't interact with them because your drop target is above them in the z-order.

Think of an HTML page as a bunch of overlapping rectangles. Mouse interactions hit the topmost layer only.

Solution 1: (workable) Remove that z-index, or set the z-index for your files list and your buttons higher than the drop target. This should work however it may create undesirable behaviors on some browsers, if the user tries to drop a file directly on your file list, or your remove buttons.

Solution 2: (recommended) Move your file list and remove buttons outside of the drop target. Design your drop target do its one function- accepting file drops, and mouse clicks that invoke the file upload action.

I had the same problem when using the sample code from MudBlazor home page https://mudblazor.com/components/fileupload#drag-and-drop-example

As Memetican states it seemed like the .drag-drop-input was overlaying the other content. I dont know what I am doing, so I will not give an explanation but the position: absolute; part caught my interest. Reading about it here led me to changing it from absolute to static. Together with some other minor changes from the sample code I have the following that seems to be working

@page "/tools/csvimport"
@inject ISnackbar Snackbar
<style>
    .drag-drop-zone {
        display: flex;
        align-items: center;
        justify-content: center;
        transition: all .4s;
        height: 100%;
    }

    .drag-drop-input {
        position: static;
        width: 100%;
        height: 100%;
        opacity: 0;
        cursor: pointer;
        z-index: 2;
    }

    .drag-enter {
        box-shadow: var(--mud-elevation-10);
    }

    .list {
        padding: 2em;
        min-width: 100%;
    }
</style>

<MudGrid Justify="Justify.Center" Spacing="4">

    <MudItem xs="12" sm="12" md="6">
        <MudPaper @ondragenter="@(()=>_dragEnterStyle="drag-enter")"
                  @ondragleave="@(()=>_dragEnterStyle=null)"
                  @ondragend="@(()=>_dragEnterStyle=null)"
                  Class=@("drag-drop-zone "+ _dragEnterStyle)
                  MinHeight="200px">

            <InputFile OnChange="OnInputFileChanged" class="drag-drop-input" />

            @if (file is null)
            {
                <MudText Typo="Typo.h6">Drag file here, or click to browse your files</MudText>
            }
            else
            {
                <MudChip Color="Color.Info">@file.Name</MudChip>
            }


        </MudPaper>
        <MudGrid Justify="Justify.Center" Spacing="4" Class="mt-4">
            <MudItem>
                <MudButton OnClick="Upload" Disabled="@(file is null)" Color="Color.Primary" Variant="Variant.Filled">Upload</MudButton>
            </MudItem>
            <MudItem>
                <MudButton OnClick="@(() => file = null)" Disabled="@(file is null)" Color="Color.Error" Variant="Variant.Filled">Clear</MudButton>
            </MudItem>
        </MudGrid>
    </MudItem>

</MudGrid>
@code {
    string _dragEnterStyle;
    IBrowserFile file;

    void OnInputFileChanged(InputFileChangeEventArgs e)
    {
        file = e.File;
    }
    void Upload()
    {
        //Upload the files here
        Snackbar.Configuration.PositionClass = Defaults.Classes.Position.TopCenter;
        Snackbar.Add("TODO: Upload " + file.Name, Severity.Normal);
    }
}