BUG #17350: GIST TRGM Index is broken when combining with combining INCLUDE with a string function (e.g. lower).

The following bug has been logged on the website:

Bug reference:      17350
Logged by:          louis jachiet
Email address:      louis.jachiet@telecom-paris.fr
PostgreSQL version: 13.4
Operating system:   Archlinux
Description:

Hello everyone,

I hope this is not a duplicate of a similar bug (I tried to check…). GIST
TRGM Index seems to return
wrong values when populated with a string function (such as lower)  and an
include. If I issue the 
following lines, instead of returning 'foo' and 'bar', postgresql will
return  two empty lines:

    CREATE EXTENSION IF NOT EXISTS pg_trgm ;
    CREATE TABLE t (a VARCHAR(50));
    INSERT INTO t VALUES ('foo') ;
    INSERT INTO t VALUES ('BAR') ;
    CREATE INDEX test_idx ON t USING gist(lower(a) gist_trgm_ops) INCLUDE
(a) ;
    set enable_seqscan=off ;
    SELECT lower(a) FROM t ;

Obviously for this last SELECT, the index is only useful because of the
seqscan=off 
but if you have a large database and issue a command like:

    SELECT 1 FROM t WHERE lower(a) LIKE '%o%' ;

then the output will be also empty because the index will return empty lines
and the recheck condition will fail.
If I use a function different than lower (e.g. upper) the problem persists
but if remove the function or if remove the
include then everything works just fine. It really seems that it is the
combination of include + string function + gist trgm
that makes the SELECT return empty lines. 

Thank you for your time!

Regards