[unified-css] Migrate `createShadowRoot` and `registerCSSFiles`.

Bug: 391381439
Change-Id: I9ce0a735ddd70ed3620ebc6ae20aa32ba18f76cd
Doc: https://goo.gle/devtools-unified-css-design
Reviewed-on: https://chromium-review.googlesource.com/c/devtools/devtools-frontend/+/6219150
Auto-Submit: Benedikt Meurer <[email protected]>
Reviewed-by: Alex Rudenko <[email protected]>
Commit-Queue: Benedikt Meurer <[email protected]>
diff --git a/front_end/panels/network/NetworkLogView.ts b/front_end/panels/network/NetworkLogView.ts
index 31d929e..9ef0ad2 100644
--- a/front_end/panels/network/NetworkLogView.ts
+++ b/front_end/panels/network/NetworkLogView.ts
@@ -65,7 +65,7 @@
   NetworkRequestNode,
 } from './NetworkDataGridNode.js';
 import {NetworkFrameGrouper} from './NetworkFrameGrouper.js';
-import networkLogViewStylesRaw from './networkLogView.css.legacy.js';
+import networkLogViewStyles from './networkLogView.css.legacy.js';
 import {NetworkLogViewColumns} from './NetworkLogViewColumns.js';
 import {
   NetworkTimeBoundary,
@@ -74,10 +74,6 @@
   NetworkTransferTimeCalculator,
 } from './NetworkTimeCalculator.js';
 
-// TODO(crbug.com/391381439): Fully migrate off of constructed style sheets.
-const networkLogViewStyles = new CSSStyleSheet();
-networkLogViewStyles.replaceSync(networkLogViewStylesRaw.cssContent);
-
 const UIStrings = {
   /**
    *@description Text in Network Log View of the Network panel
@@ -514,6 +510,7 @@
       filterBar: UI.FilterBar.FilterBar, progressBarContainer: Element,
       networkLogLargeRowsSetting: Common.Settings.Setting<boolean>) {
     super();
+    this.registerRequiredCSS(networkLogViewStyles);
     this.setMinimumSize(50, 64);
 
     this.element.id = 'network-container';
@@ -1411,8 +1408,8 @@
   }
 
   override wasShown(): void {
+    super.wasShown();
     this.refreshIfNeeded();
-    this.registerCSSFiles([networkLogViewStyles]);
     this.columnsInternal.wasShown();
   }