Let's use this id-card svg for the custom post type icon rather than a standard dashicon.
First, download the raw SVG file. If you open it up in a text editor, it should look something like this:
<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="id-card" class="svg-inline--fa fa-id-card fa-w-18" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 576 512"><path fill="currentColor" d="M528 32H48C21.5 32 0 53.5 0 80v16h576V80c0-26.5-21.5-48-48-48zM0 432c0 26.5 21.5 48 48 48h480c26.5 0 48-21.5 48-48V128H0v304zm352-232c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16c0 4.4-3.6 8-8 8H360c-4.4 0-8-3.6-8-8v-16zm0 64c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16c0 4.4-3.6 8-8 8H360c-4.4 0-8-3.6-8-8v-16zm0 64c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16c0 4.4-3.6 8-8 8H360c-4.4 0-8-3.6-8-8v-16zM176 192c35.3 0 64 28.7 64 64s-28.7 64-64 64-64-28.7-64-64 28.7-64 64-64zM67.1 396.2C75.5 370.5 99.6 352 128 352h8.2c12.3 5.1 25.7 8 39.8 8s27.6-2.9 39.8-8h8.2c28.4 0 52.5 18.5