How to show number of tables for each database in Postgres?
You can use something like the following which will list every table (with their row counts) for every schema in the database:
select n.nspname as table_schema,
       c.relname as table_name,
       c.reltuples as rows
from pg_class c
join pg_namespace n on n.oid = c.relnamespace
where c.relkind = 'r'
      and n.nspname not in ('information_schema','pg_catalog')
order by c.reltuples desc;

I believe you'll need to use dynamic SQL in order to run it in every database. Here's a walkthrough.