UPDATE Query replacing string primary key taking days to resolve
For the first query it can run fairy fast, but you'd need some temporary functional index for a join:

create index bigtable_old_id_2 on bigtable( split_part(bigtable.old_id,'.',2) );
create index foreigntable_old_id on foreigntable(old_id);


This will allow Potgres to quickly find matching row in bigtable.

You can drop these indexes afterwards if you don't need them anymore.