> Why is the domain owned by an icelandic entity instead of the nonprofit?
According to the WHOIS information, the registration of libera.chat was made 2021-04-23. This registration was made ~1 month before the organisation Libera Chat was announced. As far as I can tell, the organisation could not have made the registration as a legal entity before existing.
Seeing the registrar is Namecheap, I guess someone made the registration and made use of the zero-cost Whoisguard service available. Perhaps the registrant's contact details point to Iceland. Some of my domains point to Panama, what gives.
> Where is the company registration number of the nonprofit (required to open a bank account - where will donations be held, etc).
As the OP title suggests, Libera Chat was assembled a week ago. There is no Swedish law requiring that an organisation registers, but as you suggest, it will be necessary to register a legal entity for financial purposes. Fulfilling the paperwork of registering a non-profit organisation with Skatteverket and thus receiving an ORG number generally comes after the fact of the foundation of said organisation.
Non-profit organisations in Sweden are real and protected entities, registration or not.