How come I cannot logon to my instance as sysdba, when the ORACLE_SID variable is set correctly?

Here's a reminder if you use a symbolic link for your ORACLE_HOME variable:

You will not be able to attach to your instance using OS authentication, like under the following circumstances:

echo $ORACLE_SID
testdb01
echo $ORACLE_HOME=/orasw/oracle/product/current
ls -la /orasw/oracle/product/current
lrwxrwxrwx 1 oracle dba 12 Jan 31 08:34 /orasw/oracle/product/current -> 19.21
ls -la 
sqlplus / as sysdba

The above statement will not be able to connect to your instance.

You can, however, connect to the instance by going through the listener instead:

sqlplus sys@testdb01 as sysdba

SQL*Plus: Release 19.0.0.0.0 - Production on Wed Jan 31 08:38:42 2024
Version 19.21.0.0.0

Copyright (c) 1982, 2022, Oracle.  All rights reserved.

Enter password:

Connected to:
Oracle Database 19c Enterprise Edition Release 19.0.0.0.0 - Production
Version 19.21.0.0.0

SYS@testdb01>SQL>show user
USER is "SYS"

So in order to create a bequeath session, you need an ORACLE_HOME variable that does not use symbolic links.

See this post about IPC and bequeath sessions for more details.