Use text decoration on the editor side.

seedlet/assets/css/style-editor.css

@@ -585,9 +585,11 @@ div[data-type="core/button"] {
 }
 
 .wp-block-file .wp-block-file__textlink {
-	border-bottom: 1px solid var(--global--color-secondary);
 	color: var(--global--color-primary);
-	text-decoration: none;
+	text-decoration: underline;
+	text-decoration-thickness: 1px;
+	text-underline-offset: 3px;
+	text-decoration-color: var(--global--color-secondary);
 }
 
 .wp-block-file .wp-block-file__button-richtext-wrapper {

seedlet/assets/sass/blocks/file/_editor.scss

@@ -1,8 +1,10 @@
 .wp-block-file {
 	.wp-block-file__textlink {
-		border-bottom: 1px solid var(--global--color-secondary);
 		color: var(--global--color-primary);
-		text-decoration: none;
+		text-decoration: underline; 
+		text-decoration-thickness: 1px; // Not yet supported in Chrome
+		text-underline-offset: 3px;  // Not yet supported in Chrome
+		text-decoration-color: var(--global--color-secondary);
 	}
 
 	.wp-block-file__button-richtext-wrapper {