[headless] Add default browser context to HeadlessBrowser.

headless/app/headless_shell.cc

Index: headless/app/headless_shell.cc
diff --git a/headless/app/headless_shell.cc b/headless/app/headless_shell.cc
index 530a7c5dc3498e2d3b19d99b12c8ce6da043d47a..3d21f20190c709538ef7608b840e2d4c92dada33 100644
--- a/headless/app/headless_shell.cc
+++ b/headless/app/headless_shell.cc
@@ -75,6 +75,8 @@ class HeadlessShell : public HeadlessWebContents::Observer,
 
     HeadlessBrowserContext::Builder context_builder =
         browser_->CreateBrowserContextBuilder();
+    // TODO(eseckler): These switches should also affect BrowserContexts that
+    // are created via DevTools later.
     if (base::CommandLine::ForCurrentProcess()->HasSwitch(
             switches::kDeterministicFetch)) {
       deterministic_dispatcher_.reset(
@@ -98,6 +100,7 @@ class HeadlessShell : public HeadlessWebContents::Observer,
           }));
     }
     browser_context_ = context_builder.Build();
+    browser_->SetDefaultBrowserContext(browser_context_);
 
     HeadlessWebContents::Builder builder(
         browser_context_->CreateWebContentsBuilder());