GS/HW: Allow creation of known targets via move with offset

Fixes upscaling with subtitles in Devil May Cry.

pcsx2/GS/Renderers/HW/GSRendererHW.cpp

@@ -2310,6 +2310,24 @@ void GSRendererHW::Draw()
 				GL_INS("Skipping (%d,%d=>%d,%d) draw at FBP %x/ZBP %x due to invalid height or zero clear.", m_r.x, m_r.y,
 					m_r.z, m_r.w, m_cached_ctx.FRAME.Block(), m_cached_ctx.ZBUF.Block());
 
+				// Since we're not creating a target here, if this is the first draw to the target, it's not going
+				// to be in the height cache, and we might create a smaller size target. We also need to record
+				// it for HW moves (e.g. Devil May Cry subtitles).
+				if (!height_invalid)
+				{
+					const GSVector2i target_size = GetValidSize(nullptr);
+					if (!no_rt && is_zero_color_clear)
+					{
+						g_texture_cache->GetTargetSize(m_cached_ctx.FRAME.Block(), m_cached_ctx.FRAME.FBW, m_cached_ctx.FRAME.PSM,
+							target_size.x, target_size.y);
+					}
+					if (!no_ds && is_zero_depth_clear)
+					{
+						g_texture_cache->GetTargetSize(m_cached_ctx.ZBUF.Block(), m_cached_ctx.FRAME.FBW, m_cached_ctx.ZBUF.PSM,
+							target_size.x, target_size.y);
+					}
+				}
+
 				CleanupDraw(false);
 				return;
 			}

pcsx2/GS/Renderers/HW/GSTextureCache.cpp

@@ -3648,8 +3648,9 @@ bool GSTextureCache::Move(u32 SBP, u32 SBW, u32 SPSM, int sx, int sy, u32 DBP, u
 
 	// Beware of the case where a game might create a larger texture by moving a bunch of chunks around.
 	// We use dx/dy == 0 and the TBW check as a safeguard to make sure these go through to local memory.
+	// We can also recreate the target if it's previously been created in the height cache with a valid size.
 	// Good test case for this is the Xenosaga I cutscene transitions, or Gradius V.
-	if (src && !dst && dx == 0 && dy == 0 && ((static_cast<u32>(w) + 63) / 64) <= DBW)
+	if (src && !dst && ((dx == 0 && dy == 0 && ((static_cast<u32>(w) + 63) / 64) <= DBW) || HasTargetInHeightCache(DBP, DBW, DPSM, 10)))
 	{
 		GIFRegTEX0 new_TEX0 = {};
 		new_TEX0.TBP0 = DBP;
@@ -4107,6 +4108,31 @@ GSVector2i GSTextureCache::GetTargetSize(u32 bp, u32 fbw, u32 psm, s32 min_width
 	return GSVector2i(min_width, min_height);
 }
 
+bool GSTextureCache::HasTargetInHeightCache(u32 bp, u32 fbw, u32 psm, u32 max_age, bool move_front)
+{
+	TargetHeightElem search = {};
+	search.bp = bp;
+	search.fbw = fbw;
+	search.psm = psm;
+
+	for (auto it = m_target_heights.begin(); it != m_target_heights.end(); ++it)
+	{
+		TargetHeightElem& elem = const_cast<TargetHeightElem&>(*it);
+		if (elem.bits == search.bits)
+		{
+			if (elem.age > max_age)
+				return false;
+
+			if (move_front)
+				m_target_heights.MoveFront(it.Index());
+
+			return true;
+		}
+	}
+
+	return false;
+}
+
 bool GSTextureCache::Has32BitTarget(u32 bp)
 {
 	// Look for 32-bit targets at the matching block.

pcsx2/GS/Renderers/HW/GSTextureCache.h

@@ -502,6 +502,7 @@ public:
 	Target* FindOverlappingTarget(u32 BP, u32 BW, u32 PSM, GSVector4i rc) const;
 
 	GSVector2i GetTargetSize(u32 bp, u32 fbw, u32 psm, s32 min_width, s32 min_height);
+	bool HasTargetInHeightCache(u32 bp, u32 fbw, u32 psm, u32 max_age = std::numeric_limits<u32>::max(), bool move_front = true);
 	bool Has32BitTarget(u32 bp);
 
 	void InvalidateContainedTargets(u32 start_bp, u32 end_bp, u32 write_psm = PSMCT32);