How do I list all tables in all schemas owned by the current user in Postgresql?
This will list all tables the current user has access to, not only those that are owned by the current user:

select *
from information_schema.tables
where table_schema not in ('pg_catalog', 'information_schema')
and table_schema not like 'pg_toast%'


(I'm not entirely sure the not like 'pg_toast%' is actually needed though.)

I you really need the owner information, you probably need to use pg_class and related tables.

Edit: this is the query that includes the owner information:

select nsp.nspname as object_schema,
       cls.relname as object_name, 
       rol.rolname as owner, 
       case cls.relkind
         when 'r' then 'TABLE'
         when 'm' then 'MATERIALIZED_VIEW'
         when 'i' then 'INDEX'
         when 'S' then 'SEQUENCE'
         when 'v' then 'VIEW'
         when 'c' then 'TYPE'
         else cls.relkind::text
       end as object_type
from pg_class cls
  join pg_roles rol on rol.oid = cls.relowner
  join pg_namespace nsp on nsp.oid = cls.relnamespace
where nsp.nspname not in ('information_schema', 'pg_catalog')
  and nsp.nspname not like 'pg_toast%'
  and rol.rolname = current_user  --- remove this if you want to see all objects
order by nsp.nspname, cls.relname;