The connection tunnel you are perhaps thinking of is a walkway that is indeed landside and connects T3 to T2 going past the Heathrow Express and Underground stations en route. It’s a long walk, but perfectly walkable. However because it’s landside it does entail clearing immigration.

There is no walkable route airside. The airside connection is via bus, which isn’t long but that of course adds uncertainty and means (like clearing immigration) that the timing isn’t quite in your control.

In either case, you would need to clear security at T2, again meaning you could be delayed if queues are long.