Hi there,
try this:
.woocommerce.widget_product_search input[type="search"] {
color: #5e6679;
background-color: #ffffff;
border-color: #5e6679;
}
.woocommerce.widget_product_search input[type="search"]::placeholder {
color: #000;
}
.woocommerce.widget_product_search button {
color: #ffffff;
background-color: #5e6679;
}
.woocommerce.widget_product_search button:hover {
color: #ffffff;
background-color: #5e6679;
}
I included the ::placeholder as well.