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The following bug has been logged on the website:

Bug reference: 18246
Logged by: Alexander Lakhin
Email address: exclusion(at)gmail(dot)com
PostgreSQL version: 16.1
Operating system: Ubuntu 22.04
Description:

The following script:
CREATE EXTENSION pgstattuple;
CREATE TABLE t (a int, b int[], c int) PARTITION BY RANGE (a);

CREATE INDEX a_idx ON t USING btree(a);
CREATE INDEX b_idx ON t USING gin(b);
CREATE INDEX c_idx ON t USING hash(c);

SELECT pgstatindex('a_idx');
SELECT pgstatginindex('b_idx');
SELECT pgstathashindex('c_idx');

gives an unexpected error for the hash index:
ERROR: could not open file "pg_tblspc/0/PG_16_202307071/0/0": No such file
or directory

while for btree and hash indexes errors are more adequate:
ERROR: relation "a_idx" is not a btree index
ERROR: relation "b_idx" is not a GIN index

Reproduced on REL_12_STABLE .. master.
(On master, thanks to commit 049ef3398, which added an Assert in smgr.c,
that assertion fails.)

This anomaly can be observed since 8b08f7d48 from 2018-01-19, but IMO the
culprit is e759854a0 from 2017-02-03, which introduced the following
asymmetry in pgstatindex.c:
if (!IS_INDEX(rel) || !IS_BTREE(rel))
if (!IS_INDEX(rel) || !IS_GIN(rel))
But:
if (!IS_HASH(rel))