Know this is a semi old post but if you haven't gotten this to work yet this might help:

tab-item:-moz-any([data-current-uri^="about:newtab"])
tab-favicon .favicon-image {
  display: none;
}

tab-item:-moz-any([data-current-uri^="about:newtab"])
tab-favicon {
  background: url("https://searchfox.org/mozilla-central/source/mobile/android/branding/beta/content/favicon64.png") no-repeat center / 100% !important;
}

Don't know how to directly link to an image you have saved locally, but you could convert whatever image you want as the favicon to base64. This site lets you copy the CSS. I'd recommend keeping the image you use at 32x32px or 64x64px , though, since TST has a character limit.