refactor: split Core into EngineCore (engine) and Core (UI)

EngineCore (new app/coreengine.{h,cpp}) owns every engine-safe part of
the old Core singleton: CoreParams, lifecycle of the engine managers,
UndoStack, tool/snapping/timecode state, locale, autorecovery, recent
projects, footage filters, clipboard, project registry, type
declarations, and the proxy toggle. UI dependencies are inverted
through hooks instead: status-bar/cache-full signals and std::function
handlers for image-sequence confirmation, footage relink, OTIO import,
project save/close and layout load (same pattern as
Config::ErrorHandler).

Core (app/) now derives from EngineCore and keeps only UI behavior:
the main window, dialogs, panel heuristics, import/export flows and
project lifecycle presentation. Its public API is unchanged (all
inherited), and Core::instance() covariantly static_casts the engine
singleton. The render worker constructs EngineCore directly, making it
the first binary that no longer needs the UI side of Core.

~25 engine call sites move from core.h to coreengine.h; a dozen more
drop a vestigial core.h include (gaining direct includes for symbols
they were borrowing transitively). Full gtest suite green (1986 tests,
0 failures).

app/node/project/serializer/serializer.cpp

@@ -26,7 +26,7 @@
 #include <QXmlStreamReader>
 
 #include "common/xmlutils.h"
-#include "core.h"
+#include "coreengine.h"
 #include "node/group/group.h"
 #include "serializer190219.h"
 #include "serializer210528.h"
@@ -156,7 +156,7 @@ ProjectSerializer::Result ProjectSerializer::load(Project *project,
 ProjectSerializer::Result ProjectSerializer::paste(LoadType load_type,
 												   Project *project)
 {
-	QString clipboard = Core::paste_string_from_clipboard();
+	QString clipboard = EngineCore::paste_string_from_clipboard();
 	if (clipboard.isEmpty()) {
 		return k_no_data;
 	}
@@ -257,7 +257,7 @@ ProjectSerializer::Result ProjectSerializer::copy(const SaveData &data)
 	ProjectSerializer::Result res = ProjectSerializer::save(&writer, data);
 
 	if (res == k_success) {
-		Core::copy_string_to_clipboard(copy_str);
+		EngineCore::copy_string_to_clipboard(copy_str);
 	}
 
 	return res;