Yes, it certainly sound like DBD::Oracle couldn't load the external (propritary) libraries from instantclient.

Note: It's been a long time since i used Oracle, but DBD::Oracle was always a bit of a bear to install, because the Oracle client bins and libs and configs are just weird and do things a bit different than any other modern database.

Other people had similar problems:

• Odd Linux Instant Client issue
• ORA-12154 as oracle user, whit the root account it works fine
• DPI-1047 on CentOS 7.4 with cx_Oracle 6.4 and Oracle Instant Client 18.3 RPMs
• Python & Oracle Instant Client connection setup on Linux
• Can't locate loadable object for module DBD::Oracle
• plugin Oracle Database : working as root user but not as centreon-engine account

One thing, that trips me up sometimes for all kinds of software installations and permission/usergroup creation stuff: Using old login sessions that haven't loaded all the new permissions and environment variables. If you're stumped, it's always a good idea to close all SSH sessions and start fresh (or reboot, if it's on the local computer).

One thing i would re-check after a session refresh/reboot is that the Oracle provided command line tools (sqlplus, tnsping) still work as a normal user.

Downloading the tarball for DBD::Oracle and running "perl Makefile.PL && make test" as the non-root user might provide additional insight on what is failing.

Checking dmesg output and any selinux errors also often helps. I'm not a RedHat user, but here is a guide on how to check if selinux security is tripping you up in some way: How to read and correct SELinux denial messages

DBD::Oracle has a lot of open issues on the issue tracker. I couldn't find anything related, though, but OP might have additional info to put into the search bar.