Mostraré como crear un menú flotante usando el componente Dropdown de Bootstrap 5, Bootstrap Icons, CSS y algo de animación con Animate.css.

Insertamos los assets de Bootstrap, Jquery y Animate.css

<link href="https://cdn.jsdelivr.net/npm/bootstrap@5.0.1/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-+0n0xVW2eSR5OomGNYDnhzAbDsOXxcvSN1TPprVMTNDbiYZCxYbOOl7+AMvyTG2x" crossorigin="anonymous">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/bootstrap-icons@1.5.0/font/bootstrap-icons.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/4.1.1/animate.min.css"/>

<script src="https://code.jquery.com/jquery-3.3.1.slim.min.js" integrity="sha384-q8i/X+965DzO0rT7abK41JStQIAqVgRVzpbzo5smXKp4YfRvH+8abtTE1Pi6jizo" crossorigin="anonymous"></script>
<script src="https://cdn.jsdelivr.net/npm/bootstrap@5.0.1/dist/js/bootstrap.bundle.min.js" integrity="sha384-gtEjrD/SeCtmISkJkNUaaKMoLD0//ElJ19smozuHV6z3Iehds+3Ulb9Bn9Plx0x4" crossorigin="anonymous"></script>

Creamos los estilos css

<style>
        .floating-button {
        right: 30px !important;
        bottom: 30px !important;
        }

        .floating-button .btn:focus{
        box-shadow: none;
        }

        .floating-button .dropdown-menu.show div {
            animation: fadeInUp;
            animation-duration: 0.5s;
        }
    </style>

Finalmente creamos la estructura del menú.

<div class="dropup position-fixed floating-button">
        <button class="btn rounded-circle bg-primary py-2 mb-2" type="button" id="dropdownMenuButton1" data-bs-toggle="dropdown" aria-expanded="false">
            <i class="bi bi-plus-lg text-white"></i>
        </button>
        <ul class="dropdown-menu border-0 p-0 bg-transparent" aria-labelledby="dropdownMenuButton1">
            <div class="d-flex align-items-end flex-column justify-content-end">
                <button class="btn rounded-circle bg-secondary py-2 mb-2" type="button" id="dropdownMenuButton1">
                    <i class="bi bi-list-check text-white"></i>
                </button>
    
                <button class="btn rounded-circle bg-success py-2 mb-2" type="button" id="dropdownMenuButton1">
                    <i class="bi bi-sticky text-white"></i>
                </button>

                <button class="btn rounded-circle bg-danger py-2 mb-2" type="button" id="dropdownMenuButton1">
                    <i class="bi bi-calendar text-white"></i>
                </button>

                <button class="btn rounded-circle bg-warning py-2 mb-2" type="button" id="dropdownMenuButton1">
                    <i class="bi bi-person-plus text-white"></i>
                </button>
            </div>
        </ul>
    </div>

Y este sería el resultado: enlace

Codigo fuente: Menú Flotante.zip