What is the $ORACLE_HOME/dbs/hc_$ORACLE_SID.dat file?

In every $ORACLE_HOME/dbs folder you will find a file named hc_$ORACLE_SID.dat.

What is it, and is it essential for your instance?

Oracle Support states:

The $ORACLE_HOME/dbs/hc_.dat is created for the instance health check monitoring. It contains information used to monitor the instance health and to determine why it went down if the instance isn't up.

The file can be deleted while the instance is up, it won't cause any harm to your instance.

In earlier versions of the Oracle database software a bug existed that would trigger an ORA-7445 if the file was deleted while the database was up, but this was fixed as early as in version 11.2.

The file is created at every instance startup.

Source: What Is The $ORACLE_HOME/dbs/hc_.dat File? (Doc ID 390474.1) from Oracle Support

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.