System Information
Operating system: Windows-10-10.0.22621-SP0 64 Bits
Graphics card: NVIDIA GeForce RTX 3080/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 527.37

Blender Version
Broken: version: 3.4.0, branch: blender-v3.4-release, commit date: 2022-12-06 18:46, hash: rBa95bf1ac01be

Short description of error
Subsurf Modifier with 'Catmull-Clark' type, Limit surface toggled on detailed objects causes compositor editing lag.
Still causes lag if viewport visibility is disabled but if render visibility is toggled off the lag disappears.
The lag increases if the scene has more subsurf modifiers.

Exact steps for others to reproduce the error

1. Have a mesh that is detailed with geometry.
2. Add subsurf with limit surface on.
3. Enable compositor
4. Add a mix node and modify its value.