What are the other operations performed by a switch which are outside the VLAN's boundaries.
Is Logical (VLAN) Segregation is exactly same as breaking a switching network physically via a Router?
Using VLANs on a switch is the same thing as having multiple, unconnected switches. It takes a router to route packets between VLANs.
With a layer-2 switch, you need an external router for a device on one VLAN to communicate with a device on a different VLAN. Routers route packets between networks, while switches switch frames on the same network.
A layer-3 switch can be configured to route packets between VLANs because a layer-3 switch has a router built into it.
It seems you're asking about the control-plane of Ethernet networks. Yes, there are other, optional features of modern Ethernet-based networks, and especially for wireless networks. These aren't strictly necessary, and many Ethernet networks don't use or support any of these features.
For the wired kind, some other examples you may be looking for are:
Some of these features were once envisioned to be ubiquitous, but have only found niche use, too. LACP is pretty much only used for link aggregation (LAG) but it has troubleshooting / OAM value, and to be honest, many network management and migration chores would be easier if LACP were used more broadly.
I hope this helps somewhat answer your question and point to some of the other technologies we don't commonly work with, but that are considered to be "beneath layer-3."