Thanks! I can't find any field that specifies open or blocklist or allowlist but I do see arrays for linked and allowed and blocked. My best-guess is:
if allowed is not null, then the server's federation is in allowlist state
if blocked is not null, then the server's federation is in blocklist state
...but I could be totally wrong
And I don't know how to determine if the server's federation state is open.
It would be good if we had three example servers -- one in each state (open, blocklist, and allowlist) so that I could compare the API's output for each.
Regarding "federation state": You can have a blocklist, then Lemmy will federate with every instance except blocked ones. Or have an allowlist, then it will only federate with the allowed ones. If neither is set then it also federate with everything. Using allowlist and blocklist together doesnt make much sense, then it would only federate with allowed instances which are not in the blocklist.