Omnibox has the following APIs:

OmniboxView::ApplyCaretVisibility();
OmniboxModel::SetCaretVisibility(bool visible);

On Desktop, those are used to actually toggle the caret visibility in the omnibox. 
On iOS, we provide an empty implementation for ApplyCaretVisibility(); 

We used to call SetCaretVisibility(b) for the side effect of collecting the following metric:

- UserActionRate.MobileFocusedFakeboxOnNtp
- UserActionRate.MobileFocusedOmniboxNotOnNtp
- UserActionRate.MobileFocusedOmniboxOnNtp

But these metrics were deprecated and are not collected since M64. 

However, now we have the following metrics:

- INSTANT_NTP_WITH_FAKEBOX_AS_STARTING_FOCUS (new tab page with fakebox as starting focus)
- INSTANT_NTP_WITH_OMNIBOX_AS_STARTING_FOCUS (new tab page with omnibox as starting focus)

Those seem to be collected when an autocomplete suggestion is being opened.

The way it works is as follows: 

- OmniboxEditModel::OpenMatch(...) generates an OmniboxLog by calling ClassifyPage() and passes 
it to OmniboxEventGlobalTracker::OnURLOpened
- OmniboxMetricsProvider::OnURLOpenedFromOmnibox() is called and 
- OmniboxMetricsProvider::RecordOmniboxOpenedURL() collects the metric

So by the time OpenMatch is called, ClassifyPage() needs to know whether it was focused from 
the Fakebox or Omnibox. For this, OmniboxEditModel's focus_source_ is used. How is it set on iOS? 

When tapped on the fakebox:

1. [ContentSuggestionsHeaderViewController fakeOmniboxTapped:]
2. [ToolbarCoordinator focusFakebox]
3. ONLY ON IPAD: 
   3a. [LocationBarCoordinator focusOmniboxFromFakebox]
   3b. OmniboxEditModel::OnSetFocus()     <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
   3c. OmniboxEditModel::SetCaretVisibility(false)
4. [LocationBarCoordinator focusOmnibox]
5. [OTFI becomeFirstResponder]
6. OmniboxViewIOS::OnDidBeginEditing()
7. ONLY ON IPHONE: OmniboxEditModel::OnSetFocus()   <<<<<<<<<<<<<<<<<<<<<<<<<<<<<


When tapped on the omnibox (on NTP or any other page):

1. [OTFI becomeFirstResponder]
2. OmniboxViewIOS::OnDidBeginEditing()
3. OmniboxEditModel::OnSetFocus()

When "New Search" is tapped in Quick Actions widget:

1. MainApplicationDelegate, App State, etc
2. [BVC tabModel:newTabWillOpen:inBackground:]
3. [LocationBarCoordinator focusOmnibox]
4. [OTFI becomeFirstResponder]
5. OmniboxViewIOS::OnDidBeginEditing()
6. OmniboxEditModel::OnSetFocus()

Now, none of this actually sets the focus_source_ variable of OmniboxEditModel; but once any character is typed:

1. -[UITextFieldDelegate textFieldDidChange:] 
2. OmniboxViewIOS::OnDidChange
3. OmniboxViewIOS::OnAfterPossibleChange 
4. OmniboxEditModel::OnAfterPossibleChange
   At this state, a workaround for Linux with a TODO(samarth) (dating to 2013) is
   setting focus_source_.  


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The above calls for the following questions:
1. Does anybody care about these metrics?
2. How to better collect these metrics without relying on SetCaretVisibility() as a side effect?

For (2), I propose:

1. Expose a setter for focus_source_
2. Call the setter before OmniboxEditModel::OnAfterPossibleChange()
3. Since this way we don't go into the linux workaround of if (focus_source_ == INVALID), 
focus_source_ value is not reset and is correctly logged later.