Do Araknis switches support IPv6?
Solution 1:
A switch doesn't know about IP.
Switches forward Ethernet frames. They don't need to know anything about the protocols at higher layers.
If it is a managed switch it may have a web interface used to configure the switch over IP. Such an interface could support IPv4 or IPv6 or both. However which IP protocol you use to configure the switch doesn't influence what protocols you can use through the switch. You can even send non-IP protocols through a switch.
A managed switch may also have features going beyond switching, some of those features may operate on the IP layer. Some products take this so far that they are actually fully capable routers. Whether a specific device is acting as a switch or a router can depend on how it is configured.
The lack of IPv6 access for hosts connected to the network is unlikely to be caused by the switches, it is more likely caused by the router or the ISP not supporting IPv6.
Solution 2:
The link provided suggests that there are three levels of software switching: unmanaged, Web-based L2 and managed L2. The common point to all of these options is that the device doesn't support routing.
So - what this means is that any of these switches are going to happily pass frames, whether IPv6, IPv4 or IPX (just picking out a random non-IP example). What these switches won't do is route between different subnets (i.e. the switch won't act as the gateway for the subnet).
If you happen to connect an IPv6-enabled router (...to include the Araknis example you've mentioned) then it will be able to communicate with hosts on the L2-only switch to provide connectivity between subnets (..or to the greater Internet, if so equipped).
If v6 isn't working at your location I'd suggest focusing on the router configuration to see that there's both upstream connectivity and appropriate configuration on the interfaces. After this the question becomes proper support for RA, routing to the upstream, etc.