Industrial networks increasingly rely on Tactile Internet (TI) to enable real-time remote interaction through haptic, audio, and visual modalities, imposing stringent requirements for ultra-low latency, high reliability, and high throughput. While Network Slicing (NS) in mobile networks has been widely studied, most existing solutions rely on simulation or require extensive modifications to the 5G System (5GS), making them impractical for real-world TI deployments. This paper introduces SliceEdge, an edge-based NS that proactively classifies and isolates multi-modal traffic in campus before it enters the 5GS. By leveraging In-Network Computing (INC), SliceEdge is deployed directly on network devices, enabling slicing at the data path without altering the 5GS architecture. We develop and evaluate SliceEdge on a cloud-native 5G testbed with real datasets from bilateral teleoperation and immersive Virtual Reality (VR) applications. Experimental results demonstrate that SliceEdge achieves traffic isolation up to 37% throughput improvement, sub-5 ms latency for haptic and control traffic, and packet loss below 10^-5, meeting the stringent Key Performance Indicators (KPIs) of TI applications in industrial and campus network environments.