GS/HW: DATE setup changes.

DATE one can run on complex alpha test if there's no overlap.
Make sure DATE one doesn't run if complex alpha test is enabled and there's overlap.
Enable DATE barrier on complex alpha test if there's overlap.

Author: lightningterror

pcsx2/GS/Renderers/HW/GSRendererHW.cpp

@@ -5900,10 +5900,12 @@ void GSRendererHW::EmulateDATESelectMethod(DATEOptions& date_options, GSTextureC
 
 	const GSDevice::FeatureSupport& features = g_gs_device->Features();
 
+	// Date one can run with complex alpha test if there's no overlap.
 	const bool complex_alpha_test = m_cached_ctx.TEST.ATE &&
 	                                m_cached_ctx.TEST.ATST != ATST_ALWAYS &&
 	                                m_cached_ctx.TEST.ATST != ATST_NEVER &&
-	                                m_cached_ctx.TEST.AFAIL != AFAIL_KEEP;
+	                                m_cached_ctx.TEST.AFAIL != AFAIL_KEEP &&
+	                                m_prim_overlap != PRIM_OVERLAP_NO;
 	if (m_cached_ctx.TEST.DATM)
 	{
 		blend_alpha_min = std::max(blend_alpha_min, 128);
@@ -5946,9 +5948,15 @@ void GSRendererHW::EmulateDATESelectMethod(DATEOptions& date_options, GSTextureC
 		m_conf.require_full_barrier = true;
 		date_options.barrier = true;
 	}
+	else if (m_conf.colormask.wa && complex_alpha_test && features.feedback_loops())
+	{
+		GL_PERF("DATE: Accurate with complex alpha test.");
+		m_conf.require_full_barrier = true;
+		date_options.barrier = true;
+	}
 	// When Blending is disabled and Edge Anti Aliasing is enabled,
 	// the output alpha is Coverage (which we force to 128) so DATE will fail/pass guaranteed on second pass.
-	else if (m_conf.colormask.wa && (m_context->FBA.FBA || IsCoverageAlphaFixedOne()) && features.stencil_buffer)
+	else if (m_conf.colormask.wa && !complex_alpha_test && (m_context->FBA.FBA || IsCoverageAlphaFixedOne()) && features.stencil_buffer)
 	{
 		GL_PERF("DATE: Fast with FBA, all pixels will be >= 128");
 		date_options.stencil_one = !m_cached_ctx.TEST.DATM;