Layer 2 vs Layer 3 switches

I am a bit confused on when I need and should use a layer 2 or layer 3 switch. In the corporate network we have Aruba 3810 core switches, and all the access switches are HPE 1950 24/48 PoE+. We have 7 vlans, IT mgmt, workstations, machines, wlan, wlan-guest, wlan-guest2, VoIP. Most of the the phones are having connected the computers connected to them (built in switch).

I know about routing capabilities of layer 3 switches. But… I don’t know what happens if I have a layer 2 switch like Aruba 2530 PoE+ connected, what changes and what do I miss. Only the routing between vlans? If routing has to be enabled for the vlans/devices that are connected on the 2530 it will be done on the core switches or the 1950s?

Thanks in advance!