Are VLANs necessary for my environment?

Most of those VLANs make sense to me. It's good to split by function so a VLAN for servers, one for phones, and another for workstations makes good sense. You can then get fine control over the traffic flowing between workstations and servers.

What I don't see much point in is having VLANs for workstations on each floor. A single VLAN for all workstations would keep things nice and simple. Spanning VLANs across multiple switches/trunks probably won't be an issue for a network that small.

It's also pretty pointless to maintain a seperate VLAN for switch management. They can sit happily on the server VLAN.

Nothing magical about VLANs BTW... just separate broadcast network segments with each requiring a default gateway and the appropriate ACL configuration on network ports.

Well, could be useful to have separate VLANs for data (computers) and VoIP, so you can apply some sort of traffic prioritization. Separate VLANs for management of switches it's also useful. Separate VLANs per floor seems maybe too much for 100 Pcs, unless you plan to expand in the future.