Suppose you need to attach a logo to a specific button block. You can follow these.
#1. Find Logo URL
#2. Find Button Block ID.
In my example, we will have: #block-yui_3_17_2_1_1723015693923_4061

#3. Use this code to Custom CSS box
#block-yui_3_17_2_1_1723015693923_4061 a:after {
content: "";
background-image: url(https://cdn.pixabay.com/photo/2024/08/30/10/15/woman-9009013_1280.png);
background-size: contain;
background-repeat: no-repeat;
background-position: center center;
display: inline-block;
width: 100px;
height: 50px;
}

#4. Result

#5. If you want to move logo before text, just change
:after
in the code to
:before

#6. If you want to make logo above button text, add this extra CSS
#block-yui_3_17_2_1_1723015693923_4061 a {
flex-direction: column;
}

Result

#7. If you want to add this to Header button, use this new CSS code
a.btn:after {
content: "";
background-image: url(https://cdn.pixabay.com/photo/2024/08/30/10/15/woman-9009013_1280.png);
background-size: contain;
background-repeat: no-repeat;
background-position: center center;
display: inline-block;
width: 100px;
height: 50px;
}
a.btn {
display: flex !important;
align-items: center;
}

Result
