Clean up kResetCheckDefaultBrowser since it is no longer used

This was used to trigger a one-time reprompt for users who had
previously declined the default browser prompt. At this point, all
existing users who aren't on a web app, in a test, or using a managed
pref have this value set to false so this will never be triggered.

New users would trigger this on the second browser load (there is
a check that the user isn't in the first run) but this reset happens
before the bar is shown for the first time so it resets an empty
value.

The only case where this could trigger for a user now would be if
someone dismissed the default browser prompt before 2016 and then has
had a managed pref since 2016 and now for some reason the pref is no
longer managed. This seems to be super rare and not worth keeping this
logic around for.

Original change for context: https://source.chromium.org/chromium/chromium/src/+/cff89e9b8eeabe4ab1ae204212eb893483a51636

Bug: 325511425
Change-Id: I6c82efd532a9c2b66461949368d9a031f5a83ff1
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5303287
Reviewed-by: David Roger <[email protected]>
Commit-Queue: Alison Gale <[email protected]>
Reviewed-by: Eshwar Stalin <[email protected]>
Cr-Commit-Position: refs/heads/main@{#1263495}
diff --git a/chrome/browser/prefs/browser_prefs.cc b/chrome/browser/prefs/browser_prefs.cc
index 058feb1..631e4c4 100644
--- a/chrome/browser/prefs/browser_prefs.cc
+++ b/chrome/browser/prefs/browser_prefs.cc
@@ -1007,6 +1007,10 @@
     "hats_smartlock_device_is_selected";
 #endif  // BUILDFLAG(IS_CHROMEOS_ASH)
 
+// Deprecated 02/2024
+constexpr char kResetCheckDefaultBrowser[] =
+    "browser.should_reset_check_default_browser";
+
 // Register local state used only for migration (clearing or moving to a new
 // key).
 void RegisterLocalStatePrefsForMigration(PrefRegistrySimple* registry) {
@@ -1420,6 +1424,9 @@
   registry->RegisterInt64Pref(kHatsUnlockSurveyCycleEndTs, 0);
   registry->RegisterBooleanPref(kHatsUnlockDeviceIsSelected, false);
 #endif
+
+  // Deprecated 02/2024
+  registry->RegisterBooleanPref(kResetCheckDefaultBrowser, false);
 }
 
 void ClearSyncRequestedPrefAndMaybeMigrate(PrefService* profile_prefs) {
@@ -2686,6 +2693,9 @@
   profile_prefs->ClearPref(kHatsUnlockDeviceIsSelected);
 #endif
 
+  // Deprecated 02/2024
+  profile_prefs->ClearPref(kResetCheckDefaultBrowser);
+
   // Please don't delete the following line. It is used by PRESUBMIT.py.
   // END_MIGRATE_OBSOLETE_PROFILE_PREFS