OK, we have the answer.  It’s the same bug.  There are 4 Nominatim servers and only one of them (the one in Amsterdam) is running on fresh data, the 3 others are still querying an old dataset that was built with the bug, this is why they ignore postcodes.

It’s annoying because Nominatim is not giving reliable post codes until all servers have re-imported everything.

https://github.com/osm-search/Nominatim/issues/3031