I don't get any trace files or error messages that I can use to troubleshoot this. Just trying to select from a table (dual) I created on the local postgresql database.

SQL> select * from "dual"@localdb;
select * from "dual"@localdb
                     *
ERROR at line 1:
ORA-28500: connection from ORACLE to a non-Oracle system returned this message:
ORA-02063: preceding line from LOCALDB

Output when using isql to select from the table:

[oracle@Webserver-APEX admin]$ isql -v LOCALDB
+---------------------------------------+
| Connected!                            |
|                                       |
| sql-statement                         |
| help [tablename]                      |
| echo [string]                         |
| quit                                  |
|                                       |
+---------------------------------------+
SQL> select * from dual;
+--+
| x|
+--+
| 1|
+--+
SQLRowCount returns 1
1 rows fetched

These are all fresh installs.

Oracle Linux Server release 8.10 Postgres 17.2 Oracle Database 21c Express Edition Release Version 21.3.0.0.0 unixODBC-2.3.12 postgresql-odbc 10.03.0000-3

Contents of /usr/local/etc/odbc.ini:

[LOCALDB]
Description=Local DB
Driver=/usr/lib64/psqlodbc.so
ServerName=localhost
Username=apexreps
Password=******
Port=5432
Database=postgres
Contents of $ORACLE_HOME/hs/admin/initLOCALDB.ora

HS_FDS_CONNECT_INFO = LOCALDB 
HS_FDS_TRACE_LEVEL = DEBUG 
HS_FDS_TRACE_FILE_NAME = /tmp/hsodbc_pg_debug.trc 
HS_FDS_SHAREABLE_NAME = /usr/local/lib/libodbc.so
HS_LANGUAGE=AMERICAN_AMERICA.WE8ISO8859P1 
set ODBCINI=/usr/local/etc/odbc.ini

Contents of $TNS_ADMIN/listener.ora

LISTENER =
  (DESCRIPTION_LIST =
    (DESCRIPTION =
      (ADDRESS = (PROTOCOL = TCP)(HOST = webserver-apex.internal.cloudapp)(PORT = 1521))
      (ADDRESS = (PROTOCOL = IPC)(KEY = EXTPROC1521))
    )
  )

DEFAULT_SERVICE_LISTENER = XE
USE_SID_AS_SERVICE_LISTENER = on
SID_LIST_LISTENER=
  (SID_LIST=
      (SID_DESC=
         (SID_NAME=LOCALDB)
         (ORACLE_HOME=/opt/oracle/product/21c/dbhomeXE)
         (PROGRAM=dg4odbc)
      )
  )

Contents of $TNS_ADMIN/tnsnames.ora

XE =
  (DESCRIPTION =
    (ADDRESS = (PROTOCOL = TCP)(HOST = webserver-apex.internal.cloudapp)(PORT = 1521))
    (CONNECT_DATA =
      (SERVER = DEDICATED)
      (SERVICE_NAME = XE)
    )
  )

LISTENER_XE =
  (ADDRESS = (PROTOCOL = TCP)(HOST = webserver-apex.internal.cloudapp)(PORT = 1521))

xepdb1 = (DESCRIPTION = (ADDRESS = (PROTOCOL = TCP)(HOST = webserver-apex.internal.cloudapp)(PORT = 1521)) (CONNECT_DATA = (SERVER = DEDICATED)(SERVICE_NAME = xepdb1)))


LOCALDB  =
  (DESCRIPTION=
    (ADDRESS=(PROTOCOL=tcp)(HOST=localhost)(PORT=1521))
    (CONNECT_DATA=(SID=LOCALDB))
    (HS=OK)
  )

Output of tnsping:

[oracle@Webserver-APEX admin]$ tnsping localdb

TNS Ping Utility for Linux: Version 21.0.0.0.0 - Production on 05-FEB-2025 17:48:51

Copyright (c) 1997, 2021, Oracle.  All rights reserved.

Used parameter files:
/opt/oracle/homes/OraDBHome21cXE/network/admin/sqlnet.ora


Used TNSNAMES adapter to resolve the alias
Attempting to contact (DESCRIPTION= (ADDRESS=(PROTOCOL=tcp)(HOST=localhost)(PORT=1521)) (CONNECT_DATA=(SID=LOCALDB)) (HS=OK))
OK (0 msec)

I've bounced the listener every time I've made changes to any of the configuration files.

Command to create the database link:

SQL>  create public database link "LOCALDB" connect to "apexreps" identified by "********" using 'LOCALDB';

Database link created.