Utilizei o "tansition: 2s;" que da um efeito bacana de mudança gradual.
.apresentacao__links__link{ background-color: #0093E9; background-image: linear-gradient(160deg, #0093E9 0%, #80D0C7 100%); width: 378px; text-align: center; border-radius: 8px; font-size:24px; font-weight:600px; padding: 21.5px 0; color: black; font-family: 'Montserrat', sans-serif; text-decoration: none; box-shadow: 15px 10px 10px teal; border: 2px solid cyan; display:flex; justify-content: center; gap: 16px; padding-left: 10px; }
.apresentacao__links__link:hover{ background-color: rgb(36, 129, 166); background-image: linear-gradient(160deg, #80D0C7 0%,#0093E9 100%); width: 378px; text-align: center; border: 2px solid cyan; border-radius: 8px; font-size:24px; font-weight:600px; padding: 21.5px 0; color: white; text-shadow: 0 0 15px rgba(255,255,255,.5), 0 0 10px rgba(255,255,255,.5); font-family: 'Montserrat', sans-serif; font-size: 24px; text-decoration: none; box-shadow: none; transition: 1.5s; }