How risky would it be to use a NAS that no longer has firmware support to backup my Unraid server?

You will be fine with just a few simple things to make sure of:

• The hardware will probably be just fine.
• Just dont hang your data out on the internet . If you just need remote access to manage the NAS then a jump sever like Gucamole in a DMZ or container somhow will be great. If you want remote access to your actual data over SMB and such then options like Tailscale may be useful to you.
• Look into other backup methods like Backblaze or similar if the data has any value. You could even setup rync to another location.