Hi there,
So yes you seem to have set it up correctly. When you try to add the NameServers in namecheap something is going wrong. So my suggestion would be reach out to namecheap about this matter. - They still have LIVE CHAT option don't they? should be a quick fix.
I ran a quick check on eccosystems.ca and it seems to be resolving the namecheap default dns right now.
Though I did notice when you were adding your domain into aapanel - you put ns1.nameserver in SOA and nameserver 1 as number 2. Make sure you double check that.